STAT 101 Unit 5 Quiz

Half of the width of the confidence interval is called the __________.

margin of error

Center

mu

multimedia program was designed to improve dietary behavior among low-income women. The program was evaluated by comparing women who were randomly assigned to either an intervention and or a control group. The intervention was a 30-minute session in a computer kiosk in the Food Stamp office. One of the outcomes of the experiment was the score on a knowledge test taken about two months after the program. The researchers want to know if the mean score for the intervention group is greater than the mean score for the control group. Specify the correct number from the list below that corresponds to the appropriate null and alternative hypothesis. Null Hypothesis: [a] Alternative Hypothesis: [b]

mu1-mu2=0 mu1-mu2>0

population mean difference sample mean difference sample standard deviation of differences sample size

muD d hat SD n

A study was conducted to test if a new drug was effective in reducing the number of headaches. Two groups were formed from a sample with a history of chronic headaches. One group was given the new drug and the other was given a placebo. Of the 30 people that were given the new drug, 20 of them reported relief from their headache. Of the 50 people given the placebo, 25 of them reported relief from their headache. Specify the number from the list below that corresponds to the appropriate null and alternative hypotheses. Null Hypothesis: [a] Alternative Hypothesis: [b]

p1-p2 = 0 p1-p2>0

The Women's Health Initiative conducted a randomized experiment to see if hormone therapy was helpful or harmful for post-menopausal women. The women were randomly assigned to receive estrogen plus progestin or a placebo. After 5 years, 107 out of the 8,506 women in the hormone therapy group developed cancer, while 88 of the 8,102 women in the placebo group developed cancer. Specify the number from the list below that corresponds to the appropriate null and alternative hypotheses. Null Hypothesis: [a] Alternative Hypothesis: [b

p1-p2=0 p1-p2 not equal to 0

To study the effect of a certain pesticide on a tomato plant's vitality, two measurements were taken per plant: one before application of the pesticide and one after. Researchers are interested in the mean effect of the pesticide on the plants. What type of data will result from this study?

paired data

Due to yet another road construction project in her city, Sarah must take a detour to get from work to her house. Not convinced the detour is the shortest route, Sarah decided to perform an experiment. On each trip, she flips a coin to decide which way to go; if the coin flip is heads, she takes the detour and if it's tails, she takes her alternative route. For each trip, she records the time it takes to drive from work to her house in minutes. She repeats this procedure 13 times. Group Number Mean Std. Dev. Alter. 5 8.42 2.99 Detour 8 11.8 0.86 Calculate a 95% confidence interval for the difference between the mean travel times for the detour and alternative routes. Use t* = 2.675 and round your final answer to 3 decimal places.

(-0.288, 7.048)

Measuring the drug use of the residents of a city has always been difficult. In the past, current drug use was estimated from questionnaire responses, but due to the social stigma associated with drug use, a large amount of response bias was known to be present. A proposed method for measuring a city's current drug is to measure the amount of drugs detected in the inflow to the city's wastewater treatment facility. This method was used to compare the Marijuana usage, through the measurement of the active ingredient THC-COOH, of London versus Milan over a 3 week period. Samples were made at randomly chosen times throughout the day for 21 consecutive days in both cities. Units are mg/day/1,000 people. Summary values are given in the table below. Group Number Mean Std. Dev London 21 43.5 20.33 Milan 21 20.93 1.89 Calculate a 95% confidence interval for the difference between the mean THC-COOH values for Milan and London. Use t* = 2.084 and round your final answer to 3 decimal places.

(-15.085, -33.655)

A soft drink company is conducting research to select a new design for their can. A sample of 9 participants has been selected. Instead of a typical taste test with two different sodas, they give each participant the same soda twice. One drink is served in a predominantly red can, the other in a predominantly blue can. The order the two cans are used is chosen randomly. Participants are asked to rate each drink on a scale of 1 to 10. The mean difference between the rating of the red and blue can for the 9 participants is -0.56 with standard deviation 2.19. The company wishes to estimate the effect of the color of the can on the rating. Calculate a 95% confidence interval for the mean difference in the rating between the red and blue cans. Use t* = 2.306.

(-2.24 points, 1.12 points)

A study is conducted to determine the extent to which drinking alcohol impairs driving ability. Forty volunteers are each tested twice on a computer simulated driving course, once while sober and once while intoxicated. The tests took place over two days and the order of the treatments were randomly assigned to each volunteer. One of the variables measured is the response time (in seconds) to a certain stimuli. The mean difference in response times measured while intoxicated versus sober is 0.914 seconds with standard deviation 1.496 seconds. Calculate the 99% confidence interval for the mean difference between the response times measured while intoxicated versus sober. Use t* = 2.708.

(0.273 sec., 1.555 sec.)

A soft drink company is conducting research to select a new design for their can. A sample of 9 participants has been selected. Instead of a typical taste test with two different sodas, they give each participant the same soda twice. One drink is served in a predominantly red can, the other in a predominantly blue can. The order the two cans are used is chosen randomly. Participants are asked to rate each drink on a scale of 1 to 10. The mean difference between the rating of the red and blue can for the 9 participants is -0.56 with standard deviation 2.19. Researchers would like to determine whether or not the mean difference in ratings between the red and blue can is 0. Calculate the t-test statistic for this problem. Round your final answer to 3 decimal places.

-0.767

Obesity is seen as a growing health problem in many countries, including the United States. To determine whether or not there has been an increase in obesity in men over the past ten years, medical records for 50 randomly sampled men from the year 2000 and for 75 randomly sampled men from the year 2010 were analyzed. Out of the 50 men from 2000, 10 were assigned as obese according to their height and weight while 30 out of the 75 men from 2010 were assigned as obese. Calculate the z-test statistic for this hypothesis test. Round your final answer to 2 decimal places.

-2.34

A study was conducted to see if students from public high schools were more likely to attend public colleges compared to students from private high schools. Of a random sample of 100 students from public high schools, 60 were planning to attend a public college. Of a random sample of 100 students from private high schools, 50 of them planned to attend a public college. Calculate the z-test statistic for this hypothesis test. Round your final answer to 2 decimal places.

1.42

Due to yet another road construction project in her city, Sarah must take a detour to get from work to her house. Not convinced the detour is the shortest route, Sarah decided to perform an experiment. On each trip, she flips a coin to decide which way to go; if the coin flip is heads, she takes the detour and if it's tails, she takes her alternative route. For each trip, she records the time it takes to drive from work to her house in minutes. She repeats this procedure 13 times. Sarah wants to know if the mean driving time for the detour is different from the mean driving time for the alternative route. Summary values are given in the table below. Group Number Mean Std. Dev. Alter. 5 8.42 2.99 Detour 8 11.8 0.86 Calculate the test statistic for this hypothesis test. Round your final answer to 2 decimal places.

-2.46

A study was conducted to test if a new drug was effective in reducing the number of headaches. Two groups were formed from a sample with a history of chronic headaches. One group was given the new drug and the other was given a placebo. Of the 30 people that were given the new drug, 20 of them reported relief from their headache. Of the 50 people given the placebo, 25 of them reported relief from their headache. The test statistic is z = 1.45. Select the correct p-value for this hypothesis test.

0.0735

The Women's Health Initiative conducted a randomized experiment to see if hormone therapy was helpful or harmful for post-menopausal women. The women were randomly assigned to receive estrogen plus progestin or a placebo. After 5 years, 107 out of the 8,506 women in the hormone therapy group developed cancer, while 88 of the 8,102 women in the placebo group developed cancer. The test statistic is z = 1.03. Select the correct p-value for this hypothesis test.

0.3030

Measuring the drug use of the residents of a city has always been difficult. In the past, current drug use was estimated from questionnaire responses, but due to the social stigma associated with drug use, a large amount of response bias was known to be present. A proposed method for measuring a city's current drug is to measure the amount of drugs detected in the inflow to the city's wastewater treatment facility. This method was used to compare the Marijuana usage, through the measurement of the active ingredient THC-COOH, of London versus Milan over a 3 week period. Samples were made at randomly chosen times throughout the day for 21 consecutive days in both cities. Units are mg/day/1,000 people. Researchers want to know if the mean amount of THC-COOH in Milan is different from the mean amount of THC-COOH in London. Summary values are given in the table below. Group Number Mean Std. Dev London 21 43.5 20.33 Milan 21 20.93 1.89 Calculate the test statistic for this hypothesis test. Round your final answer to 2 decimal places.

5.47

Airborne particles such as dust and smog are a part of air pollution. To evaluate particulate pollution, measurements were made every day for 40 days in the center of a small city and at a rural location about 10 miles west of the city. Because the winds usually blow from the west, we suspect that rural readings will be generally lower than the city readings.

Paired data

As part of a study on pulse rates, a random sample of 10 study participants had their pulse rate taken and asked to sit quietly for 5 minutes. At the end of 5 minutes, their pulse rates were taken again. The mean difference between the two pulse rates for the 10 participants is -1.2 beats per minute with standard deviation of 2.97. Researchers are interested in testing whether or not the mean difference in pulse rates before and after the 5 minute waiting period is 0. Using the output below, select the correct p-value for this hypothesis test.

Prob > ItI 0.234

Measuring the drug use of the residents of a city has always been difficult. In the past, current drug use was estimated from questionnaire responses, but due to the social stigma associated with drug use, a large amount of response bias was known to be present. A proposed method for measuring a city's current drug is to measure the amount of drugs detected in the inflow to the city's wastewater treatment facility. This method was used to compare the Marijuana usage, through the measurement of the active ingredient THC-COOH, of London versus Milan over a 3 week period. Samples were made at randomly chosen times throughout the day for 21 consecutive days in both cities. Units are mg/day/1,000 people. Researchers want to know if the mean amount of THC-COOH in Milan is different from the mean amount of THC-COOH in London. Using the output below, select the correct p-value for this hypothesis test.

Prob> ItI 0.00002

A study was conducted to see if students from public high schools were more likely to attend public colleges compared to students from private high schools. Of a random sample of 100 students from public high schools, 60 were planning to attend a public college. Of a random sample of 100 students from private high schools, 50 of them planned to attend a public college. The p-value for this hypothesis test is 0.0778. What is the correct decision for this hypothesis if the significance level of the test is 0.1?

Reject the null hypothesis

The USDA uses sample surveys to produce important economic estimates. One study estimated wheat prices in July and September using independent random samples of wheat producers in the two months. Researchers want to know if the mean price in September is higher than the mean price in July. The p-value for the hypothesis test is less than 0.0001. What is the correct decision for the test?

Reject the null hypothesis

Measuring the drug use of the residents of a city has always been difficult. In the past, current drug use was estimated from questionnaire responses, but due to the social stigma associated with drug use, a large amount of response bias was known to be present. A proposed method for measuring a city's current drug is to measure the amount of drugs detected in the inflow to the city's wastewater treatment facility. This method was used to compare the Marijuana usage, through the measurement of the active ingredient THC-COOH, of London versus Milan over a 3 week period. Samples were made at randomly chosen times throughout the day for 21 consecutive days in both cities. Units are mg/day/1,000 people. What are the two independent samples?

The measurements from London and Milan

The USDA uses sample surveys to produce important economic estimates. One study estimated wheat prices in July and September using independent random samples of wheat producers in the two months. Researchers want to know if the mean price in September is higher than the mean price in July. The p-value for this hypothesis test is less than 0.0001. Select the correct interpretation of this p-value.

The probability the difference in the sample mean prices of wheat in September versus July is greater than 0.658 if the true mean price of wheat in September is the same as the true mean price of wheat in July is less than 0.0001.

Obesity is seen as a growing health problem in many countries, including the United States. To determine whether or not there has been an increase in obesity in men over the past ten years, medical records for 50 randomly sampled men from the year 2000 and for 75 randomly sampled men from the year 2010 were analyzed. Out of the 50 men from 2000, 10 were assigned as obese according to their height and weight while 30 out of the 75 men from 2010 were assigned as obese. The p-value for this hypothesis test is 0.0188. What is the correct interpretation of this p-value?

The probability the difference in the two sample proportions is less than -0.2 or greater than 0.2 if the proportion of obese men in the year 2000 is equal to the proportion of obese men in the year 2010 is 0.0188.

A soft drink company is conducting research to select a new design for their can. A sample of 9 participants has been selected. Instead of a typical taste test with two different sodas, they give each participant the same soda twice. One drink is served in a predominantly red can, the other in a predominantly blue can. The order the two cans are used is chosen randomly. Participants are asked to rate each drink on a scale of 1 to 10. The mean difference between the rating of the red and blue can for the 9 participants is -0.56 with standard deviation 2.19. Researchers would like to determine whether or not the mean difference in ratings between the red and blue can is 0. The p-value for this hypothesis test is 0.4676. Select the correct interpretation of this p-value.

The probability the sample mean difference between ratings of the red and blue can is less than -0.56 or greater than 0.56 if the mean difference is 0 is 0.4676.

The United States Department of Agriculture (USDA) uses sample surveys to produce important economic estimates. One study estimated wheat prices in July and September using independent random samples of five wheat producers in each of the two months. What are the two independent samples?

The wheat producers selected in July and in September

Measuring the drug use of the residents of a city has always been difficult. In the past, current drug use was estimated from questionnaire responses, but due to the social stigma associated with drug use, a large amount of response bias was known to be present. A proposed method for measuring a city's current drug is to measure the amount of drugs detected in the inflow to the city's wastewater treatment facility. This method was used to compare the Marijuana usage, through the measurement of the active ingredient THC-COOH, of London versus Milan over a 3 week period. Samples were made at randomly chosen times throughout the day for 21 consecutive days in both cities. Units are mg/day/1,000 people. Researchers want to know if the mean amount of THC-COOH in Milan is different from the mean amount of THC-COOH in London. Based on the data and significance level, researchers decide to reject the null hypothesis. Select the appropriate conclusion for the hypothesis test.

There is enough evidence to conclude the mean amount of THC-COOH in Milan is different from the mean amount of THC-COOH in London.

Due to yet another road construction project in her city, Sarah must take a detour to get from work to her house. Not convinced the detour is the shortest route, Sarah decided to perform an experiment. On each trip, she flips a coin to decide which way to go; if the coin flip is heads, she takes the detour and if it's tails, she takes her alternative route. For each trip, she records the time it takes to drive from work to her house in minutes. She repeats this procedure 13 times. Sarah wants to know if the mean driving time for the alternative route is different from the mean driving time for the detour. Based on the data and significance level, she decides to fail to reject the null hypothesis. Select the appropriate conclusion for this hypothesis test.

There is not enough evidence to conclude the mean driving time for the alternative route is different from the mean driving time of the detour.

The Women's Health Initiative conducted a randomized experiment to see if hormone therapy was helpful or harmful for post-menopausal women. The women were randomly assigned to receive estrogen plus progestin or a placebo. After 5 years, 107 out of the 8,506 women in the hormone therapy group developed cancer, while 88 of the 8,102 women in the placebo group developed cancer. Based on the p-value and significance level for the test, researchers made the decision to fail to reject the null hypothesis. Select the appropriate conclusion for this hypothesis test.

There is not enough evidence to conclude the proportion of women with cancer is different between the hormone therapy and placebo groups.

Obesity is seen as a growing health problem in many countries, including the United States. To determine whether or not there has been an increase in obesity in men over the past ten years, medical records for 50 randomly sampled men from the year 2000 and for 75 randomly sampled men from the year 2010 were analyzed. Out of the 50 men from 2000, 10 were assigned as obese according to their height and weight while 30 out of the 75 men from 2010 were assigned as obese. The 90% confidence interval for the difference in the proportion of obese men between the years 2000 and 2010 is (-0.3316, -0.0684). Select the correct interpretation of this confidence interval.

We are 90% confident that the proportion of men who were obese in the year 2000 is between 0.0684 and 0.3316 less than the proportion of men who were obese in the year 2010.

As part of a study on pulse rates, a random sample of 10 study participants had their pulse rate taken and asked to sit quietly for 5 minutes. At the end of 5 minutes, their pulse rates were taken again. The mean difference between the two pulse rates for the 10 participants is -1.2 beats per minute with standard deviation of 2.97. Researchers are interested in estimating the mean difference in pulse rates before and after the 5 minute waiting period for the population of study participants. The 95% confidence interval for the mean difference in pulse rates was calculated to be (-3.33 bpm, 0.93 bpm). What is the correct interpretation of the confidence interval?

We are 95% confident that the mean difference between pulse rates before and after sitting for 5 minutes is between -3.33 and 0.93 beats per minute.

A soft drink company is conducting research to select a new design for their can. A sample of 9 participants has been selected. Instead of a typical taste test with two different sodas, they give each participant the same soda twice. One drink is served in a predominantly red can, the other in a predominantly blue can. The order the two cans are used is chosen randomly. Participants are asked to rate each drink on a scale of 1 to 10. The mean difference between the rating of the red and blue can for the 9 participants is -0.56 with standard deviation 2.19. The company wishes to estimate the effect of the color of the can on the rating. The 98% confidence interval for the mean difference in the ratings was computed to be (-2.67 points, 1.55 points). What is the correct interpretation of this confidence interval?

We are 98% confident that the mean difference between the ratings of the red and blue cans is between -2.67 and 1.55 points.

Due to yet another road construction project in her city, Sarah must take a detour to get from work to her house. Not convinced the detour is the shortest route, Sarah decided to perform an experiment. On each trip, she flips a coin to decide which way to go; if the coin flip is heads, she takes the detour and if it's tails, she takes her alternative route. For each trip, she records the time it takes to drive from work to her house in minutes. She repeats this procedure 13 times. Sarah computed a 98% confidence interval for the difference of mean driving time between the detour and alternative routes to be (-1.50, 8.26). Select the correct interpretation of this confidence interval.

We are 98% confident the difference between the mean driving time of the detour and alternative routes is between -1.50 and 8.26 minutes.

Measuring the drug use of the residents of a city has always been difficult. In the past, current drug use was estimated from questionnaire responses, but due to the social stigma associated with drug use, a large amount of response bias was known to be present. A proposed method for measuring a city's current drug is to measure the amount of drugs detected in the inflow to the city's wastewater treatment facility. This method was used to compare the Marijuana usage, through the measurement of the active ingredient THC-COOH, of London versus Milan over a 3 week period. Samples were made at randomly chosen times throughout the day for 21 consecutive days in both cities. Units are mg/day/1,000 people. A 98% confidence interval for the difference between the mean THC-COOH values for Milan and London is calculated to be (-35.62, -13.12). Select the correct interpretation of this confidence interval.

We are 98% confident the mean THC-COOH amount in Milan is between 13.12 and 35.62 mg/day/1,000 people less than the mean THC-COOH amount in London.

For paired data, the two sets of values ______________.

dependent

To test the age old question if talking to plants helps them grow, horticulturists obtained 24 heirloom tomatoes. From each tomato, two seeds are selected. One of the two seeds is randomly chosen to be in the "conversation" group, the other in the "control" group. Everything about how the tomato seeds were grown was exactly the same (same amount of water, same soil type, etc. ) except the seeds chosen to be in the "conversation" group were spoken to for 3 hours a day. After 6 weeks, the height of all resulting tomato plants was measured in inches. The mean difference in the height of the plants between the conversion and control groups is 7.26 inches with a standard deviation of 9.61 inches. Using the output below, select the correct p-value for this hypothesis test.

prob>t 0.0006

Does regular exercise lead to higher a higher average VO2 Max? VO2 Max is defined as the maximum amount of oxygen, in milliliters, one can use in one minute per kilogram of body mass. A random sample of 20 college age women was selected. The V02 Max was measured for each woman as well as whether or not they exercised regularly. Researchers would like to test if there is a difference in the mean VO2 Max values of women who exercised regularly and the women who did not. What type of data will result from this study?

two independent sample data

The Women's Health Initiative conducted a randomized experiment to see if hormone therapy was helpful or harmful for post-menopausal women. The women were randomly assigned to receive estrogen plus progestin or a placebo. After 5 years, 107 out of the 8,506 women in the hormone therapy group developed cancer, while 88 of the 8,102 women in the placebo group developed cancer. Calculate a 90% confidence interval for the difference in the proportion of women who developed cancer between the hormone therapy and placebo groups.

(-0.0010, 0.0045)

A study was conducted to see if students from public high schools were more likely to attend public colleges compared to students from private high schools. Of a random sample of 100 students from public high schools, 60 were planning to attend a public college. Of a random sample of 100 students from private high schools, 50 of them planned to attend a public college. Calculate a 95% confidence interval for the difference in the proportion of students planning to attend a public college between students from public versus private high schools.

(-0.0372, 0.2372)

Forced expiratory volume (FEV) is a measure of lung capacity, in liters. Initial measurements provide a baseline value to study the impact of smoking on lung function in the population. Data are obtained on the FEV of a random sample of 100 youths in East Boston in the late 1970s. The sample mean FEV value is 2.3948 liters and the sample standard deviation is 0.80287 liters. Find the 95% confidence interval for the population mean FEV value. Use t* = 1.9842.

(2.23550 liters, 2.55411 liters)

A random sample of 176 seed harvester ants is collected and the weight of the ants recorded. The sample mean weight is 58.5 mg with a sample standard deviation of 10.22 mg. Find the 90% confidence interval for the population mean weight of seed harvester ants. Use t* = 1.6536.

(57.23 mg, 59.77 mg)

While working at Jimmy John's last week, Hal noticed that he was running out of lettuce and became suspicious that the manufacturer was underfilling the lettuce bags. To see if the bags have the stated weight of 15 pounds, he randomly selected 13 bags and found a sample mean of 14.39 pounds with a sample standard deviation of 0.539 pounds. Is this enough evidence that the bags are being underfilled? Calculate the value of the t-test statistic. Round your final answer to 2 decimal places.

-4.08

A t distribution is centered around _____________.

0

At the Barilla plant in Ames, IA, a machine fills jars of marinara sauce with a population mean of 26.2 ounces of sauce and a population standard deviation of 0.04 ounces. To ensure the machine is operating properly, a quality assurance engineer randomly samples 34 jars out of all jars produced at the plant in the last week and finds the mean amount of sauce per jar is 26.197 ounces. What is the numerical value of the standard deviation of the sampling distribution of the sample mean?

0.007

Diamond size is measured in carats. For ladies diamond rings, it is known the mean diamond size is 0.2 carats with a standard deviation of 0.057 carats. A company collected a random sample of 48 ladies diamond rings from all diamond companies and found these diamonds had a mean size of 0.204 carats. What is the numerical value of the population mean?

0.2

An F5 tornado is classified as having mean wind speeds greater than 261 mph. In an effort to classify a recent tornado, 20 wind speed measurements randomly selected from within the path of the tornado had a sample mean of 265.1 mph with a sample standard deviation of 41.09 mph. Is this enough evidence to conclude the mean wind speed of this tornado is greater than 261 mph? Calculate the value of t-test statistic. Round your final answer to 2 decimal places.

0.45

A few years ago, people tended to have relatively large CD collections. For students at a large university in the midwest (enrollment = 25,000), the mean number of CDs owned was 78 with a standard deviation of 90. To confirm these numbers, a random sample of 5,000 students from this university was collected and the size of their CD collections recorded. These particular 5,000 students had a mean CD collection size of 80 CDs. image Based on the histogram of the 5000 CD collection sizes provided above and the description of the study, which of the necessary conditions for the sampling distribution of the sample mean to follow a normal model is NOT satisfied in this study?

10% condition

The _____________ requires that the sample size be less than 10% of the population size.

10% condition

A few years ago, people tended to have relatively large CD collections. For students at a large university in the midwest, the mean number of CDs owned was 78 with a standard deviation of 90. To confirm these numbers, a random sample of 120 students from this university was collected and the size of their CD collections recorded. These particular 120 students had a mean CD collection size of 80 CDs. Based on the histogram of the 120 CD collection sizes provided above and the description of the study, which of the necessary conditions for the sampling distribution of the sample mean to follow a normal model are satisfied?

10%, Randomization, and Nearly Normal conditions

The Foley Products Company has designed a new blend of concrete they believe will be twice as strong as their current high quality concrete. This new blend of concrete is believed to produce batches with a population mean strength of 15,000 psi and a population standard deviation of 2,000 psi. To validate this belief, they collect a random sample of 49 concrete batches out of all the batches produced at their plant in a particular week. The mean strength of the random sample of 49 concrete batches is measured to be 14,731 psi. Based on the histogram of the strength of the random sample of 49 concrete batches below and the description of the study, which of the necessary conditions for the sampling distribution of the sample mean to follow a normal model are satisfied?

10%, Randomization, and Nearly Normal conditions

The Foley Products Company has designed a new blend of concrete they believe will be twice as strong as their current high quality concrete. This new blend of concrete is believed to produce batches with a population mean strength of 15,000 psi and a population standard deviation of 2,000 psi. To validate this belief, they collect a random sample of 49 concrete batches out of all the batches produced at their plant in a particular week. The mean strength of the random sample of 49 concrete batches is measured to be 14,731 psi. What is the numerical value of the sample mean?

14731

The Foley Products Company has designed a new blend of concrete they believe will be twice as strong as their current high quality concrete. This new blend of concrete is believed to produce batches with a population mean strength of 15,000 psi and a population standard deviation of 2,000 psi. To validate this belief, they collect a random sample of 49 concrete batches out of all the batches produced at their plant in a particular week. The mean strength of the random sample of 49 concrete batches is measured to be 14,731 psi. What is the numerical value of the mean of the sampling distribution of the sample mean?

15000

All other things being equal, a confidence interval for a population mean based on a sample of size _______ will be narrower than a confidence interval for the same population mean based on a sample of size _______.

18 9

All other things being equal, a confidence interval for a population mean based on a sample size _______ will be wider than a confidence interval for the same population mean based on a sample of size ________.

20 50

A few years ago, people tended to have relatively large CD collections. A random sample of 20 students from a large midwestern university was taken and the number of CDs for each student recorded in the table below. 62 71 75 59 85 66 84 63 66 77 62 63 68 79 67 71 69 63 68 64 What is the sample mean number of CDs for these students?

69.1 CDs

All other things being equal, a ________________ confidence interval for a population mean will be narrower than a ______________ confidence interval for the same population mean.

80% 95%

Having 90% confidence in a confidence interval means that in _________ of all ____________ taken randomly from this _______________ the calculated _____________ will contain the true ________________.

90% samples population confidence intervals population mean

All other things being equal, a _______________ confidence interval for a population mean will be wider than a ______________ confidence interval for the same population mean.

95% 90%

A Gallup poll examined the rate of obesity in America with a survey 86,664 randomly sampled U.S. adults. Of the adults surveyed, 23,053 said that they were obese. Researchers believe more than 24.5% of the adults in the United States are obese. A z-test statistic and p-value were calculated for the correct null and alternative hypotheses. Based on the p-value and alpha level for the test, the decision was made to reject the null hypothesis. Given this information, the difference between the true proportion of adults in the United States that are obese and 0.245 is: A. Statistically Significant B. Practically Significant

A only

In a hypothesis test, we control for the probability of committing a: A. Type I error. B. Type II error.

A only

Diamond size is measured in carats. For ladies diamond rings, it is known the mean diamond size is 0.2 carats with a standard deviation of 0.057 carats. A company collected a random sample of 48 ladies diamond rings from all diamond companies and found these diamonds had a mean size of 0.204 carats. Select the correct description of the population in this study.

All diamonds found in ladies diamond rings.

At the Barilla plant in Ames, IA, a machine fills jars of marinara sauce with a population mean of 26.2 ounces of sauce and a population standard deviation of 0.04 ounces. To ensure the machine is operating properly, a quality assurance engineer randomly samples 34 jars out of all jars produced at the plant in the last week and finds the mean amount of sauce per jar is 26.197 ounces. Select the correct description of the population in this study.

All jars filled by the machine at the Barilla plant in Ames, IA during the last week.

An ABC News Poll in 2004 surveyed 1,501 randomly selected U.S. adults and asked if they believed it is more enjoyable to be married or single. In the survey, 1126 responded that they believe it is more enjoyable to be married than single. Experts believe that more than 70% of Americans believe it is more enjoyable to be married than single. A z-test statistic and p-value were calculated for the correct null and alternative hypotheses. Based on the p-value and alpha level for the test, the decision was made to reject the null hypothesis. Given this information, the difference between the true proportion of U.S. adults who believe it is more enjoyable to be married than single and 0.7 is: A. Practically Significant B. Statistically Significant

B only

For which shape of a population distribution would you need the largest sample size to apply the Central Limit Theorem?

Heavily skewed distribution.

A few years ago, people tended to have relatively large CD collections. For students at a large university in the midwest (enrollment = 25,000), the mean number of CDs owned was 78 with a standard deviation of 90. To confirm these numbers, a random sample of 15 students from this university was collected and the size of their CD collections recorded. The mean number of CDs for this sample of students was 67. Based on the histogram of the 15 CD collection sizes provided above and the description of the study, which of the necessary conditions for the sampling distribution of the sample mean to follow a normal model is NOT satisfied in this study?

Nearly Normal condition

Shape

Normal distribution as long as all conditions hold.

While working at Jimmy John's last week, Hal noticed that he was running out of lettuce and became suspicious that the manufacturer was underfilling the lettuce bags. To see if the bags have the stated weight of 15 pounds, he randomly selected 13 bags and found a sample mean of 14.39 pounds with a sample standard deviation of 0.539 pounds. Is this enough evidence that the bags are being underfilled? Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

Null: mu = 15 alternative: mu < 15

A telecommunications equipment manufacturer was receiving complaints about low volume on long distance calls. Amplifiers are used to boost the signal at various points in the long distance lines. The boosting ability of the amplifiers is called "gain." Amplifiers are designed to have a mean gain of 10 decibels. This means that a 1 dB input singal would be boosted to a 10 dB output signal. In a random sample of 120 amplifiers from this company, the mean gain is 9.03dB with a sample standard deviation of 0.861 dB. Is this enough evidence to state the amplifiers from this company fail to have the required mean gain of 10 dB? Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

Null: mu=10 alternative: mu < 10

Population Proportion 1 Population Proportion 2 Sample Proportion 1 Sample Proportion 2 Sample size 1 Sample size 2

P1 P2 P-hat 1 p-hat 2 n1 n2

Arsenic is an element that occurs naturally in groundwater, but a mean greater than 8.0 parts per billion indicates that the groundwater has been contaminated. Local officials are concerned about a well in an area of the city near a factory. On 50 consecutive days, water was randomly sampled from the well. The mean arsenic levels of these 50 measurements was 8.34 ppb with sample standard deviation 0.823 ppb. Is this enough evidence that the groundwater has been contaminated? Using the output below, select the correct p-value for this hypothesis test.

Prob > t 0.0025

A telecommunications equipment manufacturer was receiving complaints about low volume on long distance calls. Amplifiers are used to boost the signal at various points in the long distance lines. The boosting ability of the amplifiers is called "gain." Amplifiers are designed to have a mean gain of 10 decibels. This means that a 1 dB input singal would be boosted to a 10 dB output signal. In a random sample of 120 amplifiers from this company, the mean gain is 9.03dB with a sample standard deviation of 0.861 dB. Is this enough evidence to state the amplifiers from this company fail to have the required mean gain of 10 dB? The p-value for this hypothesis test is less than 0.0001. What is the correct decision about this hypothesis test?

Reject the null hypothesis

At the Barilla plant in Ames, IA, a machine fills jars of marinara sauce with a population mean of 26.2 ounces of sauce and a population standard deviation of 0.04 ounces. To ensure the machine is operating properly, a quality assurance engineer randomly samples 34 jars out of all jars produced at the plant in the last week and finds the mean amount of sauce per jar is 26.197 ounces. Select the correct description of the sample in this study.

The 34 jars mentioned in the problem that were filled at the Barilla plan in Ames, IA during the last week and then selected and measured.

The Foley Products Company has designed a new blend of concrete they believe will be twice as strong as their current high quality concrete. This new blend of concrete is believed to produce batches with a population mean strength of 15,000 psi and a population standard deviation of 2,000 psi. To validate this belief, they collect a random sample of 49 concrete batches out of all the batches produced at their plant in a particular week. The mean strength of the random sample of 49 concrete batches is measured to be 14,731 psi. Select the correct description of the sample in this study.

The 49 concrete batches of the new blend of concrete referred to in the problem.

Diamond size is measured in carats. For ladies diamond rings, it is known the mean diamond size is 0.2 carats with a standard deviation of 0.057 carats. A company collected a random sample of 48 ladies diamond rings from all diamond companies and found these diamonds had a mean size of 0.204 carats. Select the correct description of the population mean in this study.

The mean diamond size found on all ladies diamond rings.

Diamond size is measured in carats. For ladies diamond rings, it is known the mean diamond size is 0.2 carats with a standard deviation of 0.057 carats. A company collected a random sample of 48 ladies diamond rings from all diamond companies and found these diamonds had a mean size of 0.204 carats. Select the correct description of the sample mean in this study.

The mean diamond size of the 48 ladies diamond rings referred to in the problem.

The Foley Products Company has designed a new blend of concrete they believe will be twice as strong as their current high quality concrete. This new blend of concrete is believed to produce batches with a population mean strength of 15,000 psi and a population standard deviation of 2,000 psi. To validate this belief, they collect a random sample of 49 concrete batches out of all the batches produced at their plant in a particular week. The mean strength of the random sample of 49 concrete batches is measured to be 14,731 psi. Select the correct description of the population mean in this study.

The mean strength of all batches of the new blend of concrete produced at their plant in a particular week.

At the Barilla plant in Ames, IA, a machine fills jars of marinara sauce with a population mean of 26.2 ounces of sauce and a population standard deviation of 0.04 ounces. To ensure the machine is operating properly, a quality assurance engineer randomly samples 34 jars out of all jars produced at the plant in the last week and finds the mean amount of sauce per jar is 26.197 ounces. Select the correct description of the sample mean in this study.

The mean weight of 34 jars randomly selected at the Barilla plant in Ames, IA out of all jars filled by the machine in the last week.

A study was conducted to test if a new drug was effective in reducing the number of headaches. Two groups were formed from a sample with a history of chronice headaches. One group was given the new drug and the other was given a placebo. Of the 30 people that were given the new drug, 20 of them reported relief from their headache. Of the 50 people given the placebo, 25 of them reported relief from their headache. What are the two independent samples in this study?

The placebo group and new drug group

A telecommunications equipment manufacturer was receiving complaints about low volume on long distance calls. Amplifiers are used to boost the signal at various points in the long distance lines. The boosting ability of the amplifiers is called "gain." Amplifiers are designed to have a mean gain of 10 decibels. This means that a 1 dB input singal would be boosted to a 10 dB output signal. In a random sample of 120 amplifiers from this company, the mean gain is 9.03dB with a sample standard deviation of 0.861 dB. Is this enough evidence to state the amplifiers from this company fail to have the required mean gain of 10 dB? The p-value for this hypothesis test is less than 0.0001. Select the correct interpretation of this p-value.

The probability of obtaining a sample mean of 9.03 dB or less if the true mean is 10 dB is less than 0.0001.

Arsenic is an element that occurs naturally in groundwater, but a mean greater than 8.0 parts per billion indicates that the groundwater has been contaminated. Local officials are concerned about a well in an area of the city near a factory. On 50 consecutive days, water was randomly sampled from the well. The mean arsenic levels of these 50 measurements was 8.34 ppb with sample standard deviation 0.823 ppb. Is this enough evidence that the groundwater has been contaminated? A t-test statistic and p-value were calculated for the correct null and alternative hypotheses. Based on the p-value and alpha level for the test, the decision was made to reject the null hypothesis. Given this information, select the correct conclusion of the hypothesis test below.

There is enough evidence to conclude the mean level of arsenic is greater than 8.0 ppb.

An F5 tornado is classified as having mean wind speeds greater than 261 mph. In an effort to classify a recent tornado, 20 wind speed measurements randomly selected from within the path of the tornado had a sample mean of 265.1 mph with a sample standard deviation of 41.09 mph. Is this enough evidence to conclude the mean wind speed of this tornado is greater than 261 mph? A t-test statistic and p-value were calculated for the correct null and alternative hypotheses. Based on the p-value and alpha level for the test, the decision was made to fail to reject the null hypothesis. Given this information, select the correct conclusion of the hypothesis test.

There is not enough evidence to conclude the mean wind speed of this tornado is greater than 261 mph.

What is the relationship between the significance level alpha of a hypothesis test and the probability of committing a Type I error?

They are the same

A quantitative variable is recorded and used as numbers and has units.

True

An airline claims that it rarely loses a passenger's checked luggage, and, if checked luggage is lost, 90% of the luggage is recovered and returned to the owner within 24 hours. A consumer group believes the 24-hour recovery rate of lost luggage is actually lower (worse) than the airline's claim. Assume the airline's claim that 90% of lost luggage is recovered and returned to the owner within 24 hours is true. Based on the data, if we reject the airline's claim (the null hypothesis) in favor of a recovery rate lower than 90%, we have made ________________.

Type I error

An F5 tornado is classified as having mean wind speeds greater than 261 mph. In an effort to classify a recent tornado, 20 wind speed measurements were randomly selected from within the path of the tornado. Suppose the mean wind speed for this tornado really is greater than 261 mph. Based on the data, if we fail to reject the null hypothesis that the mean wind speed is 261 mph, we have made _______________.

Type II error

A study was conducted to see if students from public high schools were more likely to attend public colleges compared to students from private high schools. Of a random sample of 100 students from public high schools, 60 were planning to attend a public college. Of a random sample of 100 students from private high schools, 50 of them planned to attend a public college. The 90% confidence interval for the difference between the proportion of students planning to attend public college between students at public versus private high schools is (-0.0152, 0.2152). Select the correct interpretation of this confidence interval.

We are 90% confident the proportion of students planning to attend public colleges who attended public high schools is between 0.0152 lower than to 0.2152 higher than the proportion of students planning to attend public colleges who attended private high schools.

The purchase of a diamond ring is a large expense, requiring advanced planning. To estimate how much you would need to spend on a diamond, a random sample of 351 diamonds is taken from the website AwesomeGems.com on July 28, 2005. The sample mean cost per carat is $6242.40 and the sample standard deviation cost is $2895.41. The 95% confidence interval for the population mean is ($5938.42, $6546.32). Select the correct interpretation of this confidence interval.

We are 95% confident the population mean cost of diamonds is between $5938.42 and $6546.32 per carat.

The Census at Schools program collects data each year from students enrolled in primary and secondary schools in many different countries. In a random sample of 100 students selected from participating schools in Canada, the sample mean arm span of boys is 157.3 cm and the sample standard deviation is 15.43 cm. The 99% confidence interval for the population mean was (153.25 cm, 161.35 cm). Select the correct interpretation of this confidence interval.

We are 99% confident the population mean arm span of boys from participating schools in Canada is between 153.25 cm and 161.35 cm.

Arsenic is an element that occurs naturally in groundwater, but a mean greater than 8.0 parts per billion indicates that the groundwater has been contaminated. Local officials are concerned about a well in an area of the city near a factory. On 50 consecutive days, water was randomly sampled from the well. Assume the water in the well has a mean arsenic level greater than 8.0 ppb. Based on the data, if we decide to reject the null hypothesis and conclude the mean arsenic level of the water is greater than 8.0 ppb, we have made ____________.

a correct decision

Select all attributes of the t-distribution.

bell-shaped unimodal symmetric

When you increase the probability of committing a Type I error, you [a] the probability of committing a Type II error. When you decrease the probability of committing a Type I error, you [b] the probability of committing a Type II error.

decrease increase

The parameter for a t distribution is the _____________.

degrees of freedom

Forced expiratory volume (FEV) is a measure of lung capacity, in liters. Initial measurements provide a baseline value to study the impact of smoking on lung function in the population. Data are obtained on the FEV of a random sample of 100 youths in East Boston in the late 1970s. The sample mean FEV value is 2.3948 liters and the sample standard deviation is 0.80287 liters. The 90% confidence interval for the population mean is (2.26156 liters, 2.52818 liters). At the 10% level, what is the correct decision for the hypothesis test with the null and alternative hypotheses below? Hnot: mu = 2.5 Ha: mu not equal to 2.5

fail to reject the null hypothesis

The Census at Schools program collects data each year from students enrolled in primary and secondary schools in many different countries. In a random sample of students selected from participating schools in Canada, the sample mean arm span of boys is 157.3 cm and the sample standard deviation is 15.43 cm. The 99% confidence interval for the population mean was (153.25 cm, 161.35 cm). At the 1% level, what is the correct decision for the hypothesis test with the null and alternative hypotheses below? Hnot: mu = 157 Ha: mu not equal to 157

fail to reject the null hypothesis

Committing a Type II error while conducting a hypothesis test means that you have _______________.

failed to reject a false null hypothesis

The population distribution is The sampling distribution of the sample mean for samples of size 10 is The sampling distribution of the sample mean for samples of size 50 is The sampling distribution of the sample mean for samples of size 100 is

fattest graph second fattest graph 2nd skinniest skinniest

When the significance level alpha of the hypothesis test is [a], it is easier to reject the null hypothesis. When the significance level alpha of the hypothesis test is [b], it is harder to reject the null hypothesis.

higher lower

When there are little to no consequences of rejecting a true null hypothesis, researchers can choose a [a] significance level alpha. When there are large consequences of rejecting a true null hypothesis, researchers should choose a [b] significance level alpha.

higher lower

When conducting inference for the difference between two proportions, the two groups must be ________________.

independent

The _______________ is the distribution of all possible ____________ calculated in repeated sampling from the population.

sampling distribution model for the sample mean sample means

For any non-normal population distribution, the Central Limit Theorem states the _________________ will follow a normal distribution for all large sample sizes.

sampling distribution of the sample mean

A few years ago, people tended to have relatively large CD collections. For students at a large university in the midwest, the mean number of CDs owned was 78 with a standard deviation of 90. To confirm these numbers, a random sample of 120 students from this university was collected and the size of their CD collections recorded. These particular 120 students had a mean CD collection size of 80 CDs. If the distribution of the number of CDs was skewed to the right with a few large outliers, the shape of the sampling distribution of the sample mean

is skewed to the right for smaller sample sizes but looks more like a normal distribution for larger sample sizes.

Population mean

mu

sample size

n

The ______________ requires the population distribution to be approximately a normal distribution for small sample sizes.

nearly normal condition

Diamond size is measured in carats. For ladies diamond rings, it is known the mean diamond size is 0.2 carats with a standard deviation of 0.057 carats. A company collected a random sample of 48 ladies diamond rings from all diamond companies and found these diamonds had a mean size of 0.204 carats. If the distribution of the size of all diamonds in ladies diamond rings follows a normal distribution, the shape of the sampling distribution for the sample mean will follow a _____________ distribution.

normal

Null -hypothesis one-sided hypothesis (right-tailed) one-sided hypothesis (left-tailed) Two-sided hypothesis (two-tailed)

p1-p2=0 p1-p2 >0 p1-p2<0 p1-p2 not equal to 0

A numerical summary of information from the population is called a

parameter

In a hypothesis test, the estimate of the common population proportion is called the _____________.

pooled sample proportion

The group of all people you want to collect information from is called the

population

The _________ is the distribution of the quantitative variable in the population. This distribution is usually ______________.

population distribution unknown

If the difference between the null hypothesis value of a parameter and the true value of the parameter is meaningful in context, this difference is called ______________.

practically significance

The significance level for a test is the same as the ___________.

probability of committing a Type I error

The mean and standard deviation are numerical summaries of ________________ variables.

quantitative

At the Barilla plant in Ames, IA, a machine fills jars of marinara sauce with a population mean of 26.2 ounces of sauce and a population standard deviation of 0.04 ounces. To ensure the machine is operating properly a quality assurance engineer samples 34 jars of sauce by selecting the first 34 jars he sees in a box. Based on the histogram and normal quantile plot provided and the description of the study, check which of the necessary conditions for the sampling distribution of the sample mean is NOT satisfied in this study?

randomization condition

The _______________ requires that the sample be selected randomly from the population.

randomization condition

The power of a hypothesis test is the probability you ________________.

reject a false null hypothesis

Committing a Type I error while conducting a hypothesis test means that you have _____________.

rejected a true null hypothesis

sample standard deviation

s

standard error

s over the square root of n

Diamond size is measured in carats. For ladies diamond rings, it is known the mean diamond size is 0.2 carats with a standard deviation of 0.057 carats. A company collected a random sample of 48 ladies diamond rings from all diamond companies and found these diamonds had a mean size of 0.204 carats. Match the description on the left with the correct distribution on the right. A histogram of the diamond size of the 48 diamonds in the sample. A histogram of the diamond size of all diamonds that can be found in ladies diamond rings. A histogram of the mean diamond size of all possible random samples of 48 diamonds taken from this population.

sample distribution population distribution model sampling distribution model

The __________________ is the distribution of the quantitative variable in the sample. This distribution is determined from the data in the ______________.

sample distribution sample

population standard deviation

sigma

variability

sigma over the square root of n

A smaller group selected from the group we want to collect information is called a

smaple

A numerical summary of information from the sample is called a

statistic

Rejecting the null hypothesis for a hypothesis test means there is a ____________ difference between the null hypothesis value of the parameter and its true value.

statistical

critical value

t*

margin of error

t* s over the square room of n

The Women's Health Initiative conducted a randomized experiment to see if hormone therapy was helpful or harmful for post-menopausal women. The women were randomly assigned to receive estrogen plus progestin or a placebo. After 5 years, 107 out of the 8,506 women in the hormone therapy group developed cancer, while 88 of the 8,102 women in the placebo group developed cancer. What are the two independent samples in this study?

the hormone therapy group and the placebo group

The confidence level of a confidence interval is related to which value?

the t* critical value

At the Barilla plant in Ames, IA, a machine fills jars of marinara sauce with a population mean of 26.2 ounces of sauce and a population standard deviation of 0.04 ounces. To ensure the machine is operating properly, a quality assurance engineer randomly samples 34 jars out of all jars produced at the plant in the last week and finds the mean amount of sauce per jar is 26.197 ounces. Assume another employee randomly selects another 34 jars and weighs the sauce in each of these. The two sample means would most likely be different from each other due to sampling ___________________.

variability

Sampling variability is the ________________.

variability expected between samples

confidence interval

y hat +- t* times s over the square root of n

sample mean

y-bar