Statistics 121 BYU Exam 2
For many years, "working full-time" has meant working 40 hours per week. Nowadays it seems that corporate employers expect their employees to work more than this amount. A researcher decides to investigate this hypothesis. The null hypothesis states that the average time full-time corporate employees work per week is 40 hours. The alternative hypothesis states that the average time full-time corporate employees work per week is more than 40 hours. To substantiate his claim, the researcher randomly selected 40 corporate employees and finds that they work an average of 43 hours per week with a standard deviation of 9.6 hours. What is the test statistic for testing the hypotheses H0: μ =40 vs. Ha: μ > 40?
1.98
What are the correct degrees of freedom for this test?
13
If the researcher wanted to have 95% confidence in the results with a margin of error of 5.1, how many students must be sampled? (Assume σ=15)
34
What is the standard error of the sample mean, x̄ ?
4.02
Calculate the test statistic for this test.
4.47
Below what score do 25% of students fall? (Round your answer to the nearest whole number)
432
Suppose the p-value was found to be 0.1629 using statistical software. What is the appropriate conclusion when α = .10?
Fail to reject the null hypothesis. We have insufficient evidence to conclude that the true mean number of calories in a hamburger is greater than 310.
True or False: If the probability of obtaining our sample data, assuming the null hypothesis were true, is large, we have enough evidence to accept the null hypothesis.
False
True or False: If there is not enough evidence to support the alternative hypothesis, we can accept the null hypothesis.
False
True or False: Interval estimation is a form of statistical inference in which we estimate an unknown parameter using a single number that is calculated from the sample data.
False
True or False: Point estimation is a form of statistical inference in which, based on the sample data, we estimate the unknown parameter of interest using a range of plausible values.
False
True or False: Statistically significant results are always of practical importance.
False
True or False: The null hypothesis is the claim that the researcher wants to prove.
False
The boxplot below is a graphical representation of the monthly costs of Internet service for a random sample of 100 users. The red band with a red dot in the center below the boxplot represents a 95% confidence interval estimate for the mean, μ, of the population. On the basis of this graph, can we say that 95% of the costs are included in the confidence interval? https://learningsuite.byu.edu/plugins/Upload/fileDownload.php?fileId=cekwQszNoWE4&service=scout&appId=student&courseID=YaMIrVrghPxY
NO
Consider the following interpretation of 99% confidence: There is a 99% probability that our interval captures the population parameter. Is this a correct interpretation?
No
Suppose we are testing the following hypotheses: H0: It is not your friend's birthday Ha: It is your friend's birthday What constitutes a Type I error for these hypotheses?
Saying "happy birthday" when it isn't their birthday
What constitutes a Type II error for these hypotheses?
Saying nothing when it is in fact their birthday
If the p-value for the test was 0.0005 < p-value < 0.001, what would you conclude at the α = 0.05 significance level, in context?
Since the p-value for this test (0.0005 < p-value < 0.001) is less than the 5% significance level, we have sufficient evidence to reject the null hypothesis and conclude that the true mean calorie amount of all 1-ounce chocolate chip cookies produced by this brand is greater than 100 calories.
A sample of 100 sales receipts is taken from two competing grocery stores. The mean amount of sales per customer for Store A is $49.60, while the mean amount of sales per customer for Store B is $50.23. Store B claims they have a higher mean total per customer than Store A. If there is no difference between the two stores, the probability of obtaining the difference (49.60 - 50.23 = 0.63) is 0.356. What is the null hypothesis?
Store A and Store B have the same mean total per customer.
True or False: If our data give results that are extremely unlikely to occur if H0 were true, then we have strong evidence against H0 and can reject it in favor of Ha.
True
True or False: In statistical hypothesis testing, we use the principle "Innocent until proven guilty".
True
True or False: Increasing the confidence level will lead to a wider margin of error.
True
True or False: Statistical inference can be defined as making generalizations about the population based on sample data
True
True or False: Statistically significant means that there is enough evidence to think that two groups do not have the exact same result, whereas practical significance can only be determined by the researcher if the results are worth acting upon.
True
True or False: Suppose we take all possible samples of the same size from a population and for each sample, we compute x̄. The mean of these x̄ values will be exactly equal to the mean of the population (μ) from which the samples were taken.
True
What is the probability that any random sample of 4 students has an average SAT math score between 400 and 625?
0.9566
Suppose we have a normal population distribution where μ = 80 and σ = 20. For random samples of size n = 100, what is the probability of getting an x̄ greater than 75?
0.9938
If we fail to reject a false null hypothesis, what type of error might we be making?
Type II error
What is the name of the quantity s/√n?
standard error of x-bar
Which one of the following is the correct representation of the margin of error when sigma is unknown?
t*(s/root n)
Suppose the officers would like a 99% confidence interval rather than a 95% interval using the same data. Fill in the blank: The 99% confidence interval will be the 95% confidence interval.
wider than
Which of the following is the correct formula for a confidence interval?
x-bar plus or minus t*(s/root n)
The sample mean,_____, is used to estimate the population mean,______.
x-bar, mu
What do we use to estimate μ?
x̄
The sample mean,_____, is used to estimate the population mean,______.
x̄, μ
Can we compute the probability that x-bar is less than 32?
No, not normally distributed, and we cannot apply CLT
All students in the US who took the ACT in 2014 had a mean score of μ=21.0. Suppose you randomly select two samples of students from this population, and you calculate the sample mean for each. Sample 1 has a size of n=40, and Sample 2 has a size of n=250. Which sample is more likely to get a sample mean of 18 or less?
Sample 1 is more likely
To estimate the average speed of cars traveling on a certain stretch of highway, officers randomly select 75 cars and record their speed. Suppose the 95% confidence interval is (68.5, 72.2). What is the appropriate interpretation of this confidence interval?
We are 95% confident that the true mean speed of cars on this certain stretch of highway is between 68.5 and 72.2 miles per hour.
Consider the following interpretation of 90% confidence level: "The probability that the mean of all axle diameters lies somewhere in the interval (0.98 cm, 1.02 cm) is 0.90." Is this interpretation of 90% confidence level correct or incorrect? Why or why not?
Incorrect. It states "probability on one specific calculated interval" rather than "confidence in the procedure".
What is the advantage of reporting the average of several measurements rather than the result of a single measurement?
The average of several measurements is more likely to be close to the true mean than the result of a single measurement.
Suppose the p-value is 0.0677. At α = 0.05, what should the researcher conclude?
Fail to reject the null hypothesis. There is insufficient evidence to conclude that the average time full-time corporate employees work per week is greater than 40 hours.
True or False: Increasing the sample size will lead to a wider margin of error.
False
True or False: When the population standard deviation, σ, is unknown, we cannot compute a confidence interval.
False
True or False: When the value of the population standard deviation is unknown, the only change that occurs in the calculation of our confidence interval is we use s rather than σ.
False
True or False: p-value gives the probability that the null hypothesis is true.
False
Suppose the t-statistic was 3.221. What would be the p-value for this test?
0.0025 < p-value < 0.005
What is the chance that a random sample of 10 donuts has a mean weight that is less than 5.6 oz?
0.0034
What is the first step in statistical hypothesis testing?
Stating the claims
What are the steps of hypothesis testing?
Stating the claims Choosing a sample and collecting data Assessing the evidence Making conclusions
A professor reported that students in a class had a mean score of 81.9 and a standard deviation of 6.1 on the final exam. A student took a random sample of 50 students and calculated the mean score to be 80.3. What is the probability that this student would get a mean of 80.3 or lower?
0.0322
What is the probability that the mean of n = 75 Pell grant awards will exceed (is greater than) $2700?
0.0418
Scores on the math portion of the SAT follow a Normal distribution with a mean of 507 and a standard deviation of 111. What is the probability that the mean SAT math score of a sample of 4 students is more than 600?
0.0465
Suppose we take a random sample of size 75. What is the probability that the mean of the 75 awards is less than $2,550?
0.1922
What is the probability that any random sample of n = 100 results in an x̄ between 77.3 and 81.1?
0.6203
What is the appropriate t test statistic for this test?
0.99
The weights of Cougar Tail donuts are known to have a normal distribution with a mean of 5.78 oz and a standard deviation of 0.21 oz. How many standard deviations away from the mean is a donut that weighs 6 oz?
1.05
Based on sample results, a 90% confidence interval for the mean servings of fruit per day consumed by grade school children is (0.21, 2.45). What is the margin of error?
1.12
What is the z* associated with 90% confidence?
1.645
Lower limit of control chart?
14.4
Refer to the previous question. In order to construct an x̄-chart for this process, what number should be used as the center line?
15.0
Upper limit of control chart?
15.6
A biologist wishes to estimate the mean number of teeth in an adult tiger shark. He wishes to generate a 99% confidence interval with a margin of error of 4 teeth. The standard deviation, σσ, is known to be 21.3. How many tiger sharks must he sample?
189
Suppose that a candy company makes a candy bar whose weight is supposed to be 50 grams, but in fact, the weight varies from bar to bar according to a Normal distribution with mean μ = 50 grams and standard deviation σ = 2 grams. The candy company sells bars in packs of 4 (n=4). Construct a control chart for this process. What is the center line of the control chart for this process?
50
What is the upper limit of the control chart for this process
53
A run of _________ or more points in a row on the same side of the center line indicates an out of control process.
9
Suppose the p-value for this test is 0.0734. What are the appropriate conclusions to make when α = 0.05?
Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean hemoglobin level of all children in Jordan is less than 12 g/dl.
True or False: To be able to safely compute a confidence interval, the only condition that must be met is that the data came from a random sample.
False
True or False: We can never compute probabilities on x̄ when the population is skewed.
False
True or False: When sigma is unknown it is impossible to compute a confidence interval for μ
False
A university administrator obtains a report of the academic records of past scholarship athletes at the university. From the report the administrator believes that the mean GPA (grade point average) of current male scholarship athletes is 3.02. If a researcher believes that the mean GPA of male athletes is significantly different than 3.02, what type of test should be conducted?
Two-sided test
Suppose we are testing H0: μ = 50 versus Ha: μ < 50. The upper right hand curve represents the sampling distribution of x̄ when H0 is true; the lower left hand curve represents the sampling distribution of x̄ when Ha is true. What is the color of the area that represents power if μ really is 45? https://learningsuite.byu.edu/plugins/Upload/fileDownload.php?fileId=7R2FG-YJn3KN&service=scout&appId=student&courseID=YaMIrVrghPxY
Green
A recent study claimed that half of all college students "drink to get drunk" at least once in a while. Believing that the true proportion is much lower, the College Alcohol Study interviews an SRS of 14,941 college students about their drinking habits and finds that 7,352 of them occasionally "drink to get drunk". What type of statistical inference is this?
Hypothesis testing
One of your professors claims 90% of BYU students are currently enrolled in a religion course. To test this claim, you randomly sample 300 BYU students and find that only 78% of them are enrolled in a religion course. Based on these sample results, you have evidence against your professor's claim. What type of statistical inference did you use?
Hypothesis testing
An article claims that teenagers on average will check their cellphones 150 times in one day. A student decides to test this claim using the hypotheses H0: μ = 150 vs. Ha: μ ≠ 150. A 95% confidence interval for the true mean is found to be (154.3, 167.5). On the basis of this interval, what should the student conclude at α=0.05?
The true mean is not equal to 150 since the claimed value, 150, is not in the interval.
Is the normality condition met for this test?
Yes, since the sample size is large
Fill in the blanks: The larger the sample size, the the degrees of freedom, and the the t distribution is to a normal z distribution.
higher, closer
What does s/root n estimate?
standard deviation of the sampling distribution of x-bar
What is the symbol for the sample mean?
x̄
Calculate a 95% confidence interval for the true population mean, μ.
(109.24, 131.48)
The IQ level of students at a particular university has an unknown mean. A simple random sample of 100 students is found to have a sample mean IQ of x̄=115 and a sample standard deviation of s=15. Calculate a 95% confidence interval for the mean IQ level of all students in this university.
(112,118)
Calculate a 95% confidence interval for the mean number of calories for all large orders of fries.
(548.37, 571.63)
Suppose the t test statistic was 2.94. What is the appropriate p-value for this test?
-.005<p-value<0.01
What is the t* associated with 98% confidence and df = 37?
2.457
The Federal Pell Grant Program provides need-based grants to low-income undergraduate and certain postbaccalaureate students to promote access to postsecondary education. According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2,600. Assume that the standard deviation, σ, in Pell grant awards was $500. Suppose we take random samples of size 75. What will the mean of the sampling distribution of x̄ be?
2600
A researcher is interested in the mean height of all fifth graders in Utah. She randomly samples 35 students and calculates a sample mean of 49 inches. She then computes a 90% confidence interval of (47.89 in, 50.11 in). Which of the following is a correct interpretation of a 90% confidence level?
90% of all possible confidence intervals, calculated using the same procedure as we used to obtain the interval (47.89 in, 50.11 in), will contain the true mean height, μ, of all fifth graders in Utah.
Refer to the 98% confidence interval estimate of (0.87 g/ml, 0.97 g/ml) given in the previous question. Which one of the following is a correct interpretation of 98% confidence level?
98% of time, using the same procedure as we used to obtain the interval (0.87 g/ml, 0.97 g/ml), we will obtain confidence intervals that contain the true value of μ.
The sampling distribution of x-bar gives ______ from all possible samples of the same size from the same population
All x-bar values
Suppose the p-value is 0.0367. What is the correct interpretation of this p-value?
Assuming the null hypothesis is true, there is a 0.0367 probability of obtaining a sample statistic as extreme or more extreme than what we calculated.
What would be an example of a Type I error in the context of this problem?
Believing that the mean NAEP math score is higher than 275 when it is not actually higher
What is the probability of making a Type II error?
Beta
Suppose we have an extremely left-skewed population with a mean of 45 and a standard deviation of 7. For random samples of size 15, what will the shape of the sampling distribution of x¯be?
Cannot be determined - CLT doesn't apply
Fast food chain claims that a large order of french fries has 540 calories. To test the claim that the true mean is actually higher, a sample of 15 large orders of french fries is taken. The sample mean is x̄ = 560 and the sample standard deviation is s = 21. Since the sample size is small, how could we check the condition of normality for this test?
Check a plot of the data for a single peak and no outliers
What is the quantity t*?
Confidence multiplier
The label of a certain brand of 1-ounce chocolate chip cookies states that the cookies contain 100 calories. To prevent it from exceeding 100 calories, a quality engineer routinely samples their cookies and checks the calorie content. A random sample of 14 1-ounce chocolate chip cookies resulted in the following calorie amounts: https://learningsuite.byu.edu/plugins/Upload/fileDownload.php?fileId=EkcF56RHRMPA&service=scout&appId=student&courseID=YaMIrVrghPxY Assume that σ is unknown and the calorie amounts are normally distributed. The data yield an x̄ = 120.36 and an s = 19.26. At α = 0.05, is there sufficient evidence to conclude that the average calorie content of 1-ounce chocolate chip cookies produced by this brand is greater than 100 calories? What are the appropriate hypotheses for this procedure
H0: μ = 100 calories and Ha: μ > 100 calories
Suppose the researcher actually believed the true mean is much lower than 3.02. What type of test should be conducted?
One-sided lower-tailed test
With a p-value of 0.287, what is the appropriate conclusion to make?
Our data do not provide strong enough evidence for rejecting H0
Suppose the student analyzes the data and finds that the probability of obtaining the following difference (17.4 - 20), if the true mean actually is 20 minutes, is 0.012. What is the appropriate conclusion at α=0.05?
Our data provides strong evidence for rejecting H0
Based on sample results, researchers estimate that μ, the mean height of all female students in a university, is 64 inches. What type of inference is being used?
Point estimation
Researchers want to estimate the amount of time teenagers spend watching television during one week. A random sample of 500 teenagers yielded a sample mean of 12.60 hours of television per week. What type of statistical inference is being used?
Point estimation
Suppose the correct p-value was .002 < p-value < .005 . What is the appropriate conclusion to make at α = 0.05?
Reject the null hypothesis and conclude that we have sufficient evidence to conclude that the mean score is greater than 275.
What is the parameter of interest?
The proportion of all BYU students currently enrolled in a religion course
Are the conditions for this test met? Why or why not?
Yes, because it was a random sample and n>30
Fill in the Blank: The _______ hypothesis generally represents what the researcher wants to prove, or suspects might actually be the case.
alternative
Refer to the situation in Question 7. Suppose we took samples of size 45. What will the shape of the sampling distribution of x̄ be?
approximately normal
Two researchers used the same sample data to investigate the impact of an energy awareness campaign on the mean monthly energy consumption per household of a large city. Researcher A did a lower-tailed test and Researcher B did a two-sided test. The p-value corresponding to Researcher A's test was found to be 0.030. What would be the correct conclusion to make for Researcher B's test at α = 0.05?
p-value is greater than α = 0.05, therefore, we fail to reject the null hypothesis
What is the formula for the standard error of x-bar?
s/root n
When sigma is unknown, what is the standard error of x-bar
s/root n
Suppose a sample of size 250 was taken instead of size 100. How will the margin of error change?
the margin of error will decrease in size
What is the calculated t-statistic for this test?
3.96
Suppose the p-value is 0.0367. At α = 0.05, what should the public health official conclude?
Reject the null hypothesis. The true mean hemoglobin level of all children in Jordan is less than 12 g/dl.
Suppose we have a very right skewed population distribution where μ = 80 and σ = 20. For random samples of size n = 100, what is the mean of the sampling distribution of x̄?
Equal to 80
2 rules for a process being in or out of control
-any points outside of the control limits -a run of 9 or more consecutive points on the same side of the center line
Suppose the test statistic was 2.67. What is the associated p-value?
.0025 < p-value < .005
Suppose the test statistic is 1.37. What is the p-value for this one-sided test?
.05 < p-val < .10
Suppose the same student took another sample, this time of size 100, and calculated the mean. What is the probability that the student would get a mean of 84 or higher?
0.0003
Suppose the calculated test statistic is t = -2.16. Assuming all conditions are met, what is the p-value for this left-tailed test?
0.01 < p-value < 0.02
Suppose we take a sample of size n = 50 from this same population, and we calculate x̄ = $2,800. How many standard deviations, sigma/root n , away from μ is this sample mean?
2.83
We suspect that, on average, students will score higher on their second attempt at the SAT mathematics exam than their first attempt. Here are the results for 46 randomly chosen high school students: -0|76655 -0|444333333221111 0|000011222333 0|555666789 1|00223 Should we use a z-test or a t-test on this data? Why?
A t-test because the population standard deviation is unknown, but we have the data to calculate the sample standard deviation
Suppose the p-value is 0.135. What is the correct interpretation of this p-value?
Assuming the null hypothesis is true, there is a 0.135 probability of obtaining a sample statistic as extreme or more extreme than what we calculated.
Consider the following interpretation of 90% confidence level: "90% of all possible confidence intervals computed using the same procedure used to obtain (0.98, 1.02) will contain the value of μ." Is this interpretation of 90% confidence level correct or incorrect? Why or why not?
Correct. It is stated in terms of the confidence interval procedure - not one specific, calculated interval.
Hemoglobin is a protein in the red blood cells that carries oxygen from the lungs to body tissues. People with less than 12 grams of hemoglobin per deciliter of blood (g/dl) are anemic. A public health official in Jordan suspects that the mean hemoglobin level for all children is less than 12 grams. He took a random sample of 50 children and found x̄ = 11.5 g/dl and s = 1.6 g/dl. What are the appropriate hypotheses?
H0: μ = 12 vs. Ha: μ < 12
The National Assessment of Educational Progress (NAEP) is administered annually to 4th, 8th, and 12th graders in the United States. On the math assessment, a score above 275 is considered an indication that a student has the skills to balance a checkbook. Believing that the true mean score is much higher, a researcher takes a random sample of 500 young men between the ages of 18 and 20 and calculates the mean NAEP math score of the sample to be 280. The standard deviation of math scores for the sample of young men was 25. What are the appropriate null and alternative hypotheses?
H0: μ = 275 vs. Ha: μ > 275
A fast food chain claims their regular hamburgers have an average of 310 calories. One consumer believes this average is actually much higher and takes a random sample of 45 hamburgers. The mean of this sample is x̄ = 314 and standard deviation is s = 27. What are the appropriate hopotheses?
H0: μ = 310 vs. Ha: μ > 310
To discourage students from driving to campus, a university highlighted a study that claims that students spend an average of 20 minutes looking for a parking spot. Students believe the actual time is less than this. After taking a random sample of 45 students, a researcher calculates a sample mean of 17.4 minutes to find a parking spot. In order to assess the evidence provided by the sample data, what is the appropriate question to ask?
How likely is it that, in a sample of 45, the true mean amount of time needed to find a parking spot is 17.4 minutes or less if the true mean is 20?
In order to assess the evidence provided by the sample data, what is the appropriate question to ask?
How likely is it to observe a mean GPA difference of 0.09 or more extreme if there is no difference in the mean GPA for male and female scholarship athletes?
For many years, "working full-time" has meant working 40 hours per week. Nowadays it seems that corporate employers expect their employees to work more than this amount. A researcher decides to investigate this hypothesis. The null hypothesis states that the average time full-time corporate employees work per week is 40 hours. The alternative hypothesis states that the average time full-time corporate employees work per week is more than 40 hours. To substantiate his claim, the researcher randomly selected 250 corporate employees and finds that they work an average of 47 hours per week with a standard deviation of 3.2 hours. In order to assess the evidence, what do we need to ask?
How likely it is that, in a sample of 250, we will find that the mean number of hours per week full-time corporate employees work is as high as 47 if the true mean is 40?
A study of child preferences for milk chocolate was performed. Based on sample results, researchers were 95% confident that the proportion of children that liked milk chocolate was between 0.75 and 0.93. What type of inference is being used?
Interval estimation
Based on sample results, we are 90% confident that the mean travel time to work for workers 16 and older is between 16.8 and 25.4 minutes. What type of inference is this?
Interval estimation
The Federal Pell Grant Program provides need-based grants to low-income undergraduate and certain postbaccalaureate students to promote access to postsecondary education. According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2,600. Assume that the standard deviation, σσ, in Pell grant awards was $500 and that the distribution of awards is left skewed. Suppose we take a random sample of size 20. What is the probability that the mean of the 20 awards is greater than $2,700?
It is not appropriate to calculate probabilities in this situation
Suppose we have a very right skewed population distribution where μ = 80 and σ = 20. For random samples of size n = 100, what is the standard deviation of the sampling distribution of x̄?
Less than 20
A university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that the mean GPA (grade point average) of a random sample of 40 male scholarship athletes is 3.02 and the mean GPA of a random sample of 36 female scholarship athletes is 3.11. If there is no difference in the mean GPA of male and female athletes, the probability of obtaining this difference (3.11 - 3.02 = 0.09) or more extreme is approximately 0.287. What is the null hypothesis?
Male and female scholarship athletes have the same mean GPA.
Store B does not agree with the results of the study. After looking into it, the manager discovers that receipts were taken from the first 100 shoppers at each store on a certain day of the week. Based on this information, should Store B trust the results of this study?
No, because the receipts were not collected randomly.
A researcher wishes to estimate the mean amount of money single, undergraduate college students spend on food in a typical month. To generate a sample, she calls the first 120 students listed in the directory of the local college. Is it safe to compute a confidence interval from this sample?
No- the sample was not collected randomly
Is the randomness condition met for this test?
Randomness is met because a random sample was taken from chocolate chip cookies made by this brand.
The weight of a carton of a dozen eggs produced by a certain breed of hens is supposed to be normally distributed with a mean of 780 grams. A quality manager randomly checks thirty-five cartons of eggs (n = 35) to see whether the mean weight differs from 780 grams. She finds x̄ = 796 grams and computes a 95% confidence interval estimate for the mean weight of all cartons to be (787.82 grams, 804.18 grams). On the basis of this interval, at α = 0.05, what can she conclude about H0: μ = 780 versus Ha: μ ≠ 780?
Reject H0 since 780 is outside the given interval.
suppose α =0.10 rather than 0.05. What should the researcher conclude?
Reject the null hypothesis. The average time full-time corporate employees work per week is greater than 40 hours.
With a p-value of 0.356, what is the appropriate conclusion to make?
The data does not provide strong enough evidence to reject H0
Suppose the correct answer is 56 sharks (it isn't), but the researcher can only afford to sample 25 sharks. If he wishes to maintain a 99% confidence level, what effect will this have on the resulting confidence interval?
The margin of error will be larger, resulting in a wider interval
A student takes a random sample of freshman at BYU and records their age at their first kiss. He calculates a 95% confidence interval of (17.5, 18.9). What parameter is the student trying to estimate?
The mean age at first kiss for all BYU freshmen
What is the alternative hypothesis in this example?
The mean amount of time needed to find a parking spot is less than 20 minutes.
Hemoglobin is a protein in the red blood cells that carries oxygen from the lungs to body tissues. People with less than 12 grams of hemoglobin per deciliter of blood (g/dl) are anemic. A public health official in Jordan suspects that the mean hemoglobin level for all children is less than 12 grams. He took a random sample of 50 children and found x̄ = 11.5 g/dl and s = 1.6 g/dl. What is the parameter of interest?
The mean hemoglobin level of all children in Jordan
what statistic is used to estimate the parameter of interest?
The mean level of nitrogen oxide of a sample of cars of a particular model in the very large fleet.
What is the parameter the researchers are trying to estimate?
The mean number of hours each week all teenagers spend watching television
If the p-value is less than α, then the results are statistically significant.
True
A manufacturing process produces bags of cookies. The weights of these bags are known to be Normally distributed and should have a mean of μ = 15.0 ounces with a standard deviation of σ = 0.4 ounces. In order to monitor the process, four bags are selected periodically and their average weight (x̄) is computed. What is the parameter of interest?
The mean weight of all bags of cookies produced by this manufacturing process.
The Federal Pell Grant Program provides need-based grants to low-income undergraduate and certain postbaccalaureate students to promote access to postsecondary education. According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2,600. Assume that the standard deviation, σ, in Pell grant awards was $500. If we take samples of size 200 rather than 75, what will happen to the mean of the sampling distribution of x̄?
The mean will stay exactly the same.
If all possible samples of size 20 are taken instead of size 100, how would this change the mean and standard deviation of the sampling distribution of x̄?
The mean would stay the same and standard deviation would increase
If all possible samples of size 80 are taken from a population instead of size 20, how would this change the mean and standard deviation of the sampling distribution of x̄?
The mean would stay the same and the standard deviation would decrease
Two studies were done on the same set of data, where study I was a one-sided test and study II was a two-sided test. The p-value of the test corresponding to study I was found to be 0.030. What is the p-value for study II?
The p-value must be 0.060
What is the statistic you are using to estimate the parameter of interest?
The proportion of BYU students in your sample currently enrolled in a religion course
If we take samples of size 200 rather than 75, what will happen to the standard deviation of the sampling distribution of x̄?
The standard deviation will decrease.
What is the parameter of interest in this study?
The true mean calorie amount of all 1-ounce chocolate chip cookies produced by this brand.
What is the purpose of a statistical control chart?
To distinguish between natural and unnatural variation
Fill in the Blank: Assuming that sigma is known, when we decrease our sample size and maintain our level of confidence, our margin of error becomes .
Wider
Consider the following interpretation of 99% confidence: 99% of intervals calculated with this method will capture the population parameter. Is this a correct interpretation?
Yes
https://learningsuite.byu.edu/plugins/Upload/fileDownload.php?fileId=sJPjJJHOk0dT&service=scout&appId=student&courseID=YaMIrVrghPxY samples n=20 x-bar = 68 standard deviation of 12
Yes, all points are within control limits and there isn't a run of 9 or more consecutive points on the same side of the center line.
The following sample means were collected by taking random samples of size n = 25. These sample means were computed from samples taken from a Normal population with μ = 52.4 and σ = 7.5. On the basis of these sample means, can we conclude that the process is "in control"? https://learningsuite.byu.edu/plugins/Upload/fileDownload.php?fileId=NT-cwv4kvau3&service=scout&appId=student&courseID=YaMIrVrghPxY
Yes, because all of the means vary between the lower and upper control limits
Suppose we take a sample of size n = 100 from this same population. Can we compute the probability that x̄ is greater than $2,800?
Yes, because the Central Limit Theorem applies. Thus, the sampling distribution of x-bar is normally distributed.
Can we say that the condition of "normality of the population" is met? Why or why not?
Yes, because the plot has no extreme outliers
Suppose we take a sample of size n = 10 from this same population. Can we compute the probability that x̄ is greater than 75?
Yes, because the population is normally distributed. Thus, the sampling distribution of x-bar is normally distributed.
What is the symbol for the population standard deviation?
sigma
In confidence interval estimation, we use a confidence interval to estimate
the value of a population parameter
The Federal Pell Grant Program provides need-based grants to low-income undergraduate and certain postbaccalaureate students to promote access to postsecondary education. According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2,600. Assume that the standard deviation, σ, in Pell grant awards was $500. For samples of size 75, what will the standard deviation of the sampling distribution of x̄ be?
$57.74
What is the lower limit of the control chart for this process
47
parameter
numerical fact about the population Ex: mu= average GPA of all full-time BYU students
If we take random samples of size 75 from this population, what will the shape of the sampling distribution of x̄ be?
Approximately normal
Suppose we have a very right skewed population distribution where μ = 80 and σ = 20. For random samples of size n = 100, what is the shape of the sampling distribution of x̄?
Approximately normal
According to the Central Limit Theorem, for random samples, what is the approximate shape of the sampling distribution of x̄ when the population distribution is non-Normal?
Approximately normal if the sample size is large enough
Can we say that 95% of the ages are included in the interval (17.5, 18.9)?
No
The following sample means were collected by taking random samples of size n = 25. These sample means were computed from samples taken from a Normal population with μ = 52.4 and σ = 7.5. On the basis of these sample means, can we conclude that the process is "in control"? https://learningsuite.byu.edu/plugins/Upload/fileDownload.php?fileId=iXn5GgktUqDE&service=scout&appId=student&courseID=YaMIrVrghPxY
No, because at least one of the means is either below the lower control limit or above the upper control limit.
Suppose the student is only able to sample 25 students from the class. Can he still calculate the probability of getting an average test score higher than 84? Why or why not?
No, because the sample size is not large enough
The following sample means were collected by taking random samples of size n = 25. These sample means were computed from samples taken from a Normal population with μ = 52.4 and σ = 7.5. On the basis of these sample means, can we conclude that the process is "in control"? https://learningsuite.byu.edu/plugins/Upload/fileDownload.php?fileId=PiOeHw14CI_B&service=scout&appId=student&courseID=YaMIrVrghPxY
No, because there is a run of nine or more x̄'s either above the center line or below the center line.
https://learningsuite.byu.edu/plugins/Upload/fileDownload.php?fileId=vxdovPtbd_nw&service=scout&appId=student&courseID=YaMIrVrghPxY samples n=20 x-bar = 68 standard deviation of 12
No, there are points outside the control limits
https://learningsuite.byu.edu/plugins/Upload/fileDownload.php?fileId=XyAvUzcSG_tR&service=scout&appId=student&courseID=YaMIrVrghPxY samples n=20 x-bar = 68 standard deviation of 12
No, there is a run of 9 or more consecutive points on the same side of the center line.
For small random samples from a Normal population distribution, the shape of the sampling distribution of x̄ is __________.
Normal
An administrator in a very large company wants to estimate the mean level of nitrogen oxides (NOX) emitted in the exhaust of a particular car model in their very large fleet of cars. Historically, nitrogen oxide levels have been known to be Normally distributed with a standard deviation of 0.15 g/ml. What is the parameter of interest that the administrator wants to estimate?
The mean level of nitrogen oxide of all cars of a particular model in the very large fleet.
What is the statistic you are using to estimate the parameter of interest?
The mean number of hours each week teenagers in their sample spent watching television
An administrator in a very large company wants to estimate the mean level of nitrogen oxides (NOX) emitted in the exhaust of a particular car model in their very large fleet of cars. Historically, nitrogen oxide levels have been known to be Normally distributed. A 98% confidence interval estimate for the mean nitrogen oxide level was computed. What do we hope to find in this confidence interval?
The value of μ, the mean level of nitrogen oxides emitted by all cars of a particular model in their fleet.
True or False: Suppose we take all possible samples of the same size from a population and for each, we compute x̄. The standard deviation of these x̄ values will be less than or equal to the standard deviation of the population from which the samples were taken.
True
True or False: The purpose of a confidence interval is to estimate the value of a population parameter.
True
True or False: The sampling distribution of x̄ created from small random samples from a Normally distributed population is Normal.
True
True or False: The symbol for the sample standard deviation is "s".
True
Suppose the 95% confidence interval estimate for the mean monthly cost for Internet service for all Internet users is ($19.90, $21.90). Which of the following is a correct interpretation of this 95% confidence interval?
We are 95% confident that the mean monthly cost for Internet service paid by all Internet users is between $19.90 and $21.90.
A professor is interested in the mean amount of money BYU students spend on groceries per week. He randomly samples 200 students and calculates a sample mean of $42. He then computes a 95% confidence interval of ($34.2, $49.8). Which of the following is a correct interpretation of this confidence interval?
We are 95% confident that the true mean amount of money BYU students spend on groceries per week is between $34.2 and $49.8.
suppose the correct computation of the 98% confidence interval estimate is (0.87 g/ml, 0.97 g/ml). Which of the following is a correct interpretation of this 98% confidence interval?
We are 98% confident that the value of the mean nitrogen oxide level, μ, for all cars of a particular model is between 0.87 g/ml and 0.97 g/ml.
The BYU Testing Center is known for being the location with the most prayers said per capita. Researchers asked a random sample of 47 BYU students to estimate the number of prayers they said in the BYU Testing Center last semester. The researchers are willing to consider these 47 BYU students as an SRS from the population of all BYU students. Researchers plan to use these data to estimate the mean number of prayers said by students last semester in the BYU Testing Center with 99% confidence. Suppose the confidence interval turned out to be (8.001, 13.829). What is an appropriate interpretation of this interval?
We are 99% confident that the true mean number of prayers said in the BYU Testing Center by all BYU students last semester is between 8.001 and 13.829 prayers.
Suppose we take samples of size 40 from a population with a mean of 200 and a standard deviation of 50. Can we compute the probability that x̄ is greater than 270?
Yes, because the sampling distribution of x̄ is normally distributed
statistic
numerical fact about the sample Ex: x-bar = average GPA of the 170 students in our sample
