ISA 225 Exam 1 Problem Set
Historically the average time for a customer at a coffee shop to be served is 140 seconds. In an effort to reduce this time the owners implement new procedures. After implementation they randomly sample 25 customer wait times and get an average of 120 seconds and a standard deviation of 20 seconds. Wait time is known to follow a normal distribution. You then perform the hypothesis test, Ho: μ = 140 vs Ha: μ < 140. For this situation the value of the test statistic t is:
-5.00
The standard normal probability distribution has a mean of _______ and a standard deviation of _______.
0 1
If the area under the standard normal curve to the left of z= −1.72 is 0.0427, then what is the area under the standard normal curve to the right of z = 1.72? A. 0.7642 B. 0.9573 C. 0.0427 D. 0.4573
0.0427
At your school, 6% of the class are marketing majors. You are randomly assigned to two partners in your statistics class. a) What is the probability that the first partner will be a marketing major? b) What is the probability that the first partner won't be a marketing major? c) What is the probability that both will be marketing majors? d) What is the probability that at least one will be a marketing major?
0.06 0.94 0.0036 0.1164
An automobile manufacturer offers a warranty on all new car purchases. The warranty covers the battery for the first three years. In the past, only 10% of batteries required replacement under warranty. Consider 5 cars manufactured by this company. What is the probability that only the fifth car will require a new battery under the warranty? Round answer to 3 decimal places.
0.066
You take a random sample of size 36 from a normal population and find y-bar = 90 with a standard deviation = 24. When you test Ho: μ = 95 vs Ha: μ ≠ 95 the p-value is _________ (Remember this is a two-sided test).
0.1057
Multigenerational families can be categorized as having two adult generations such as parents living with adult children, "skip" generation families, such as grandparents living with grandchildren, and three or more generations living in the household. A survey was conducted on multigenerational households. The reported results appear in the accompanying table. Use the table to complete parts a through c below. 2 Adult Gens 2 Skip Gens 3 or More Gens White 512 48 226 786 Hispanic 144 2 146 292 Black 118 36 96 250 Asian 54 13 43 110 828 99 511 1438 a) What is the probability that a multigenerational family is Hispanic? b) What is the probability that a multigenerational family selected at random is a Black, two-adult generation family? c) What type of probability did you find in part a? d) What type of probability did you find in part b?
0.203 0.082 Marginal Joint
There were 400 purchases made at a Pizza shop in the last month. Of the purchases, 360 included pizza and 108 included both pizza and salad. Find the Confidence for the rule (Pizza) -> (Salad).
0.30
An automobile manufacturer offers a warranty on all new car purchases. The warranty covers the battery for the first three years. In the past, only 10% of batteries required replacement under warranty. Consider 5 cars manufactured by this company. What is the probability that at least one of the cars will require a new battery under the warranty?
0.41
An automobile manufacturer offers a warranty on all new car purchases. The warranty covers the battery for the first three years. In the past, only 10% of batteries required replacement under warranty. Consider 5 cars manufactured by this company. What is the probability that none of the cars will require a new battery under the warranty?
0.59
For a sales promotion, the manufacturer places winning symbols under the caps of 29% of all its soda bottles. If you buy a six-pack of soda, what is the probability that you win something?
0.872
For any probability density function, what value is always the total area under the curve?
1
A student group runs a marketing campaign to try to increase student participation in intramural sports. Historically, 20% of students have participated. If a random sample of 500 students has 125 intramural participants, what is the value of the test statistic for a hypothesis test: Ho: p = 0.20 vs HA: p > 0.20 ? Round final answer to 2 decimal places, but do not use intermediate rounding.
2.8
Suppose that in a certain community, the probability of a randomly selected individual having red hair is 0.08 and the probability of a randomly selected individual being left-handed is 0.15. What additional information would be needed to find the probability of randomly selecting an individual in this community who has red hair or is left-handed? A. We would need to know the percentage of individuals in the community who have red hair and are left-handed. B. We would need to know the percentage of individuals in the community who do not have red hair. C. We would need to know the percentage of individuals in the community who are right-handed. D. No additional information is needed.
A
Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. From research on other college campuses, you believe the proportion will be near 25%. What sample size is needed if you wish to be 95% confident that your estimate is within 0.02 of the true proportion?
A sample size of 1801 is needed.
Which of the following is a correct explanation of what a confidence interval is? A. A confidence interval is a range of values used to estimate the true value of a population parameter. The confidence level is the probability the interval actually contains the population parameter, assuming that the estimation process is repeated a large number of times. B. A confidence interval gives two values (called the lower bound and upper bound) that the population mean could be with a certain level of confidence. C. A confidence interval indicates how far off we're willing to be from the population mean with a certain level of confidence. D. A confidence interval gives a range of possible values for the mean of those in the sample with a certain level of confidence. E. A confidence interval gives an exact value for the population mean with a certain level of confidence.
A. A confidence interval is a range of values used to estimate the true value of a population parameter. The confidence level is the probability the interval actually contains the population parameter, assuming that the estimation process is repeated a large number of times.
Ronnie randomly sampled 80 college students, 50 living a dorm and the other 30 living in an apartment. She asked each how much they spent on food and beverages (non-alcoholic) within the last 7 days. A 95% confidence interval for the difference in the mean amount spent on food and drinks over the past 7 days between students living in a dorm and students living in an apartment (dorm−apartment) is (−$25.80,−$11.20). Which of the following is a correct interpretation of this confidence interval? A. We are 95% confident that college students living in dorms spent between $11.20 and $25.80 less on food and drinks over the past 7 days, on average, than college students living in apartments. Your answer is correct. B. We are 95% confident that college students living in dorms spent between $11.20 and $25.80 more on food and drinks over the past 7 days, on average, than college students living in apartments. C. We are 95% confident that all college students living in dorms spent between $11.20 and $25.80 less on food and drinks over the past 7 days than all college students living in apartments. D. We are 95% confident that all college students living in dorms spent between $11.20 and $25.80 more on food and drinks over the past 7 days than all college students living in apartments.
A. We are 95% confident that college students living in dorms spent between $11.20 and $25.80 less on food and drinks over the past 7 days, on average, than college students living in apartments. Your answer is correct.
The Empirical Rule tells the approximate percentage of the data which falls into certain ranges. To which distributions does the Empirical Rule apply? Only standard normal distributions Only uniform distributions Any continuous distribution Any normal distribution
Any normal distribution
Doug randomly sampled 30 weather forecasters from around the country and kept track of how far away the actual high temperature was for a day from their predicted high temperature for the day. (Positive values mean that their predicted high temperature was higher than the actual high temperature.) Doug believed that weather forecasters always predicted temperatures higher than what actually happened because people like warmer temperatures. He obtained a sample mean of 0.5 degrees Fahrenheit. His hypotheses were H0: μx=0°F and HA: μx>0°F. He performed a hypothesis test and obtained a p-value of 0.20. What does this mean? A. The probability that the true mean is more than 0°F for all weather forecasters around the country is 0.20. B. Of all the random samples of 30 weather forecasters, 20% would give a sample mean of 0.5°F or more given that the true mean for all weather forecasters around the country is 0°F. C. The probability that the true mean is 0°F for all weather forecasters around the country is 0.20. D. Of all the random samples of 30 weather forecasters, 20% would produce a sample mean equal to the population mean.
B. Of all the random samples of 30 weather forecasters, 20% would give a sample mean of 0.5°F or more given that the true mean for all weather forecasters around the country is 0°F.
Researchers wondered if the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs, which is known to be 12.2 degrees Celsius. A survey of 31 streams without tailed frogs was taken and the water temperature was recorded for each stream. Which of the following is the correct statement of what a Type I Error is in the context of this problem? A. Researchers found no evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs and there really was no difference in the average temperatures. B. Researchers found evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs when there was no difference in the average temperatures. C. Researchers found no evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs when there was a difference in the average temperatures. D. Researchers found evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs and there really was a difference in the average temperatures.
B. Researchers found evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs when there was no difference in the average temperatures.
Before using the normal model to represent a data set, first check that the shape of the data's distribution is what shape? Both symmetric and unimodal Symmetric Unimodal Centered at zero and symmetric
Both symmetric and unimodal
Which of the following statements is not equivalent to the others? A. Of those who are male, 35% have never married. B. There is a 35% chance that a randomly selected man has never married. C. 35% of individuals who have never married are male. D. 35% of individuals who are male have never married.
C
A. Since both sample sizes are small, the manager would have to believe that all delivery times for both routes are normally distributed in order for the delivery times used in the samples to be representative of all delivery times for both routes. B. Because the sample of days to take route 1 and route 2 were chosen randomly, the distribution of the difference in sample means will be approximately normal. C. Since both sample sizes are small, the manager would have to believe that all delivery times for both routes are normally distributed in order for the distribution of the difference in sample means to be normal. D. Since both sample sizes are small, the distribution of the difference in sample means will not be normal regardless of the shape of the distributions of all delivery times for both routes.
C. Since both sample sizes are small, the manager would have to believe that all delivery times for both routes are normally distributed in order for the distribution of the difference in sample means to be normal.
Is the nutritional information listed on food items accurate? Researchers randomly sampled 12 frozen dinners of a certain type from production during a particular period. The calorie content was determined. The stated calorie content on the package was 240 calories. Researchers wanted to determine if there was evidence to indicate that the mean calorie count was not equal to 240 calories using the one-sample t-methods. Which of the following statements is true? A. Since the sample size is less than 30, the population data cannot be normally distributed. Therefore, the distribution of sample means will not be normally distributed. B. The distribution of sample means will not be normal regardless of the shape of the data in the population because the sample size is less than 30. C. The distribution of sample means will be normal only if the population data (that is, calorie content of all frozen dinners of this type produced during this particular period) follow a normal distribution. D. The distribution of sample means will be normal regardless of the shape of the data in the population (that is, calorie content of all frozen dinners of this type produced during this particular period).
C. The distribution of sample means will be normal only if the population data (that is, calorie content of all frozen dinners of this type produced during this particular period) follow a normal distribution.
A fast food store manager is testing new procedures hoping to reduce the average time to serve customers. The manager randomly samples 50 service times and uses this data to perform the following hypothesis test. Ho: μ= 182 seconds vs HA: μ< 182 seconds. In the context of this situation a Type II error would be: Concluding to implement the new procedures when in fact they work Concluding average service time has not been reduced when in fact it has been reduced Concluding average service time has been reduced when in fact it has not Concluding not to permanantly implement the new procedures when in fact they do not work
Concluding average service time has not been reduced when in fact it has been reduced
The vice-president of operations wondered if the average strength of wire cables was different between those produced at the company's plant in a rural location and those produced in the company's plant located in a large city. Which of the following is the correct statement of what a Type II Error is in the context of this problem? A. The VP had evidence to say that there was a difference in the average cable strengths between the two locations when in fact there was no difference in the average strengths. B. The VP did not have evidence to say that there was a difference in the average cable strengths between the two locations and there really was no difference in the average strengths. C. The VP had evidence to say that there was a difference in the average cable strengths between the two locations and there really was a difference in the average strengths. D. The VP did not have evidence to say that there was a difference in the average cable strengths between the two locations when in fact there was a difference in the average strengths.
D. The VP did not have evidence to say that there was a difference in the average cable strengths between the two locations when in fact there was a difference in the average strengths.
The Addition Rule P(E or F)=P(E)+P(F) applies only to which type of events? Independent Complementary Dependent Disjoint
Disjoint
Which probability method requires that the probability experiment be performed and uses the results to estimate the probability of a particular outcome? Classical Empirical (relative frequency) Subjective All of the above
Empirical (relative frequency)
A financial advising firm creates a quality initiative to decrease the percentage of documentation that contains errors. Historically, 5% of documents contain some type of error. What hypothesis statements would you use to determine if the initiative was effective?
Ho: p = 0.05 vs HA: p < 0.05
Which of the following assumptions/conditions must be met to find a 95% confidence interval for a population mean? Independence Assumption Sample size condition: n > 30 Sample size condition: np & nq > 10 n < 10% of population size Random sampling
Independence Assumption Sample size condition: n > 30 n < 10% of population size Random sampling
The Multiplication Rule P(E and F)=P(E)•P(F) applies only to which type of events? Independent Complementary Disjoint Dependent
Independent
A freshman in college wanted to determine if the "Freshman 15" is true. That is, this student wanted to determine if freshmen in college gain more than 15 pounds during their freshman year. She randomly selected 50 freshmen during the first week of school at the beginning of the year and weighed them. During finals week of the last term of the year, she weighed the same 50 students. She recorded the weight change of each-a positive value indicated a weight gain while a negative value indicated a weight loss during the year. Based on her sample, a 95% confidence interval for the average weight change of freshmen during their freshman year is (8.9,12.1) lbs. What conclusion can be made based on this confidence interval? A. It appears the the "Freshman 15" is true. That is, it appears that freshmen gain more than 15 pounds during their freshman year, on average, since both bounds are less than 15. B. There is evidence to say that freshmen gain 15 pounds, on average, during their freshman year since 15 is not in the confidence interval. C. It appears that the "Freshman 15" is not true. That is, it appears that freshman do not gain more than 15 pounds during their freshman year, on average, since the upper bound is less than 15. Your answer is correct. D. No conclusions can be made about the "Freshman 15." That is, it is unknown if freshmen gain more than 15 pounds on average or not during their freshman year.
It appears that the "Freshman 15" is not true. That is, it appears that freshman do not gain more than 15 pounds during their freshman year, on average, since the upper bound is less than 15. Your answer is correct.
A student group runs a marketing campaign to try to increase student participation in intramural sports. Historically, 20% of students have participated. A random sample of 500 students results in a p-value = 0.003 for the hypothesis test: Ho: p = 0.20 vs HA: p > 0.20. What is the conclusion in context for α = 0.05? Statistical evidence that the proportion of students participating in intramural sports is more than 20%. The campaign was not successful. Fail to Reject Ho. Reject Ho. Statistical evidence that the proportion of students participating in intramural sports is more than 20%. The campaign was successful.
Statistical evidence that the proportion of students participating in intramural sports is more than 20%. The campaign was successful.
In Market Basket Analysis, the Lift Ratio is used to avoid concluding an association when the items sets are really independent. How will you know if there is an association?
The Lift Ratio is greater than 1.
Just before a referendum on a school budget, a local newspaper polls 350 voters in an attempt to predict whether the budget will pass. Suppose that the budget actually has the support of 55% of the voters. What's the probability the newspaper's sample will lead them to predict defeat? Be sure to verify that the assumptions and conditions necessary for your analysis are met.
The probability is 0.030
If the area to the left of a z-score is less than 0.5, what must be true? A. The z-score must be equal to zero. B. The z-score must be positive. C. The z-score must be equal to one. D. The z-score must be negative.
The z-score must be negative.
Decide if the following statement is true or false and explain your answer. P(Z<2.50)=P(Z≤2.50)
True; these two probabilities are equal because there is no area under the standard normal curve associated with a single value.
A random sample of Miami University students finds that 100 of the 500 sampled participate in intramural sports. Find a 95% confidence interval for the true proportion of all students that participate in intramural sports.
[0.165, 0.235]
A developer wants to know if the houses in two different neighborhoods were built at roughly the same time. She takes a random sample of six houses from each neighborhood and finds their ages from local records. The accompanying table shows the data for each sample (in years). Complete parts a through e below Neighborhood 1 Neighborhood 2 45 40 54 54 67 52 47 35 48 36 51 53 a) Find the sample means for each neighborhood. b) Find the estimated difference of the mean ages of the two neighborhoods, y1−y2. c) Find the sample variances for each neighborhood. d) Find the sample standard deviations for each neighborhood. e) Find the standard error of the difference of the two sample means.
a) y1 = 52 y2 = 45 b) 7 years c) 64, 80 d) 8, 8.94 e) 4.9
For a certain candy, 5% of the pieces are yellow, 15% are red, 10% are blue, 15% are green, and the rest are brown. a) If you pick a piece at random, what is the probability that it is brown? it is yellow or blue? it is not green? it is striped? b) Assume you have an infinite supply of these candy pieces from which to draw. If you pick three pieces in a row, what is the probability that they are all brown? the third one is the first one that is red? none are yellow? at least one is green?
a) The probability that it is brown is 0.55. The probability that it is yellow or blue is . 15.15. The probability that it is not green is . 85.85. The probability that it is striped is 0. b) The probability of picking three brown candies is 0.166. The probability of the third one being the first red one is 0.108. The probability that none are yellow is 0.857. The probability of at least one green candy is 0.386.
An insurance company checks police records on 587 accidents selected at random and notes that teenagers were at the wheel in 95 of them. a) Create a 95% confidence interval for the percentage of all auto accidents that involve teenage drivers. b) Explain what your interval means. A. We are 95% confident that the percent of accidents involving teenagers is 16.2%. B. We are 95% confident that the true percentage of accidents involving teenagers falls inside the confidence interval limits. C. There is a 95% probability that this interval contains the true percentage of accidents involving teenagers. D. We are 95% confident that a randomly sampled accident would involve a teenager a percent of the time that falls inside the confidence interval limits. c) Explain what "95% confidence" means. d) A politician urging tighter restrictions on drivers' licenses issued to teens says, "In one of every five auto accidents, a teenager is behind the wheel." Does the confidence interval support or contradict this statement?
a) (13.2%, 19.2%) b) We are 95% confident that the true percentage of accidents involving teenagers falls inside the confidence interval limits. c) About 95% of random samples of size 587 will produce confidence intervals that contain(s) the true proportion of accidents d) The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is outside the interval.
A developer wants to know if the houses in two different neighborhoods were built at roughly the same time. She takes a random sample of six houses from each neighborhood and finds their ages from local records. The accompanying table shows the data for each sample (in years). Assume that the data come from a distribution that is Normally distributed. Complete parts a through c below. Neighborhood 1 Neighborhood 2 51 32 48 36 52 33 53 35 50 43 46 49 a) Find a 95% confidence interval for the mean difference, μ1−μ2, in ages of houses in the two neighborhoods. b) Is 0 within the confidence interval? c) What does the confidence interval suggest about the null hypothesis that the mean difference is 0?
a) (5.01, 18.99) b) No c) Reject H0 since 0 is not a plausible value for the true mean difference.
An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via "smart phones", so they want to estimate the proportion of users who access the site that way (even if they also use their computers sometimes). They draw a random sample of 100 investors from their customers. Suppose that the true proportion of smart phone users is 43%. a) What would the standard deviation of the sampling distribution of the proportion of the smart phone users be? b) What is the probability that the sample proportion of smart phone users is greater than 0.43? c) What is the probability that the sample proportion is between 0.39 and 0.46? d) What is the probability that the sample proportion is less than 0.37?
a) 0.050 b) 0.5 c) 0.514 d) 0.115
A market analyst wants to know if the new website he designed is showing increased page views per visit and calculates the summary statistics in the table to the right. Assume that the new website is website 1 and the old website is website 2. Test the hypothesis that the mean number of page views from the two websites is the same. You may assume that the number of page views from each website follow a Normal distribution. Complete parts a through c below. Website 1 Website 2 n 90 95 mean 7.5 6.5 s 4.1 4.4 t= 1.600 a) Calculate the P-value of the statistic given that the approximation formula gives df=183.0. b) Calculate the P-value of the statistic using the rule that df=min(n1−1, n2−1). c) What do you conclude at α=0.05?
a) 0.056 b) 0.057 c) Fail to reject H0 for both cases. There is not sufficient evidence to reject the claim that the mean number of page visits is the same for the two websites, in favor of the claim of increased page visits.
Nonissue Serious Concern Total Democratic 60 440 500 Republican 260 240 500 Independent 70 130 200 Total 390 810 1200 a) What is the probability that a randomly selected registered voter who is a Republican believes that global warming is a serious issue? b) What is the probability that a randomly selected registered voter is a Republican given that he or she believes global warming is a serious issue? c) What is P(Serious Concern|Democratic)?
a) 0.48 b) 0.296 c) 0.88
A market analyst wants to know if the new website he designed is showing increased page views per visit. A customer is randomly sent to one of two different websites, offering the same products, but with different designs. The data is shown in the table to the right. Complete parts a through c below. Website 1 Webiste 2 n_1 65 n_2 85 yBar_1 6.7 yBar_2 6.1 s_1 5.1 s_2 5.3 a) Find the estimated mean difference, y1−y2, in page visits between the two websites. b) Find the standard error of the estimated mean difference. c) Calculate the t-statistic for the observed difference in mean page visits assuming that the true mean difference is 0.
a) 0.6 pages b) 0.85 pages c) t = 0.71 pages
A developer wants to know if the houses in two different neighborhoods were built at roughly the same time. She hires an assistant to collect a random sample of houses from each neighborhood and finds that the summary statistics for the two neighborhoods are as shown. Complete parts a through c below. Neighborhood 1 Neighborhood 2 n_1 40 n_2 35 yBar_1 55.1 yBar_2 44.1 s_1 7.58 s_2 7.09 a) Find the estimated mean age difference, y1−y2, between the two neighborhoods. b) Find the standard error of the estimated mean difference. c) Calculate the t-statistic for the observed difference in mean ages assuming that the true mean difference is 0
a) 11 years b) 1.69 years c) t = 6.50 years
For parts a and b, use technology to estimate the following. a) The critical value of t for a 98% confidence interval with df=7. b) The critical value of t for a 95% confidence interval with df=109.
a) 3.00 b) 1.98
The police department of a major city needs to update its budget. For this purpose, they need to understand the variation in their fines collected from motorists for speeding. As a sample, they recorded the speeds of cars driving past a location with a 20 mph speed limit, a place that in the past has been known for producing fines. The mean of 100 representative readings was 23.78 mph, with a standard deviation of 3.52 mph. a) How many standard deviations from the mean would a car going the speed limit be? b) Which would be more unusual, a car traveling 32 mph or one going 12 mph?
a) A car traveling at the speed limit is 1.07 standard deviations from the mean. b) The car traveling 12 mph is more unusual. It is 3.35. standard deviations from the mean, while the car traveling 32 mph is 2.34 standard deviations from the mean.
Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. For a random sample of 42 weekdays, daily fees collected averaged $131, with standard deviation of $13. a) What assumptions must you make in order to use these statistics for inference? A. The sample size is at least 10% of the population. B. The data are a random sample of all days. C. The distribution is unimodal and symmetric with no outliers. D. The data values should be dependent. b) Find a 95% confidence interval for the mean daily income this parking garage will generate. c) Explain in context what this confidence interval means. d) Explain what 95% confidence means in this context.
a) B and C b) ($126.95, $135.05) c) There is 95% confidence that the interval contains the mean daily income. d) 95% of all samples of size 42 produce intervals that contain the mean daily income.
Sam ran an experiment to test optimum power and time settings for microwave popcorn. His goal was to deliver popcorn with fewer than 10% of the kernels left unpopped, on average. He determined that power 9 at 4 minutes was the best combination. To be sure that the method wassuccessful, he popped 8 more bags of popcorn(selected atrandom) at this setting. All were of highquality, with the percentages of unpopped kernels shown below. 10.5 9.8 2.9 10.2 5.2 12.2 6.5 6.9 a) Choose the correct null and alternative hypotheses. b) Calculate the test statistic. c) Calculate the P-value. d) Does this provide evidence that Sam met his goal?
a) H0: μ=10 HA: μ<10 b) t = -1.776 c) P-value = 0.0595 d) No, there is not enough evidence suggest that less than 10% of the kernels are left unpopped when the specified power and time settings are used.
Police recorded the average speed of cars driving on a busy street by a school. For a sample of 36 speeds, it was determined that the average amount over the speed limit for the 36 speeds was 11.9 mph with a standard deviation of 9 mph. The 95% confidence interval estimate for this sample is 8.85 mph to 14.95 mph. a) What is the margin of error for this problem? b) What size sample is needed to reduce the margin of error to no more than ±2?
a) The margin of error is 3.05 mph. b) The sample size should be at least 78 speeds.
A survey of 164 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take notes. The result of the survey is that 82 of the 164 students responded "yes." An approximate 98% confidence interval is (0.409, 0.591). a) How would the confidence interval change if the confidence level had been 95% instead of 98%? b) How would the confidence interval change if the sample size had been 410 instead of 164? c) How would the confidence interval change if the confidence level had been 99% instead of 98%? d) How large would the sample size have to be to make the margin of error one third as big in the 98% confidence interval?
a) The new confidence interval would be narrower. The new confidence interval would be (0.424,0.576). b) The new confidence interval would be narrower. The new confidence interval would be (0.443,0.557). c) The new confidence interval would be wider. The new confidence interval would be (0.400,0.601) d) The new sample size would have to be 1476
In a recent year, a research organization found that 495 of 755 surveyed male Internet users use social networking. By contrast 693 of 947 female Internet users use social networking. Let any difference refer to subtracting male values from female values. Complete parts a through d below. Assume that any necessary assumptions and conditions are satisfied. a) Find the proportions of male and female Internet users who said they use social networking. b) What is the difference in proportions? c) What is the standard error of the difference? d) Find a 99% confidence interval for the difference between these proportions.
a) The proportion of male Internet users who said they use social networking is 0.6556. The proportion of female Internet users who said they use social networking is 0.7318. b) 0.0762 c) 0.0225 d) (0.018, 0.134)
In a recent year, a research organization found that 338 of the 499 respondents who reported earning less than $30,000 per year said they were social networking users. At the other end of the income scale, 334 of the 557 respondents reporting earnings of $75,000 or more were social networking users. Let any difference refer to subtracting high-income values from low-income values. Complete parts a through d below. Assume that any necessary assumptions and conditions are satisfied. a) Find the proportions of each income group who are social networking users. b) What is the difference in proportions? c) What is the standard error of the difference? d) Find a 99% confidence interval for the difference between these proportions.
a) The proportion of the low-income group who are social networking users is 0.6774. The proportion of the high-income group who are social networking users is 0.5996.
A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect repair shop has certified as okay. They will revoke the shop's license if they find significant evidence that the shop is certifying vehicles that do not meet standards. a) In this context, what is a Type I error? b) In this context, what is a Type II error? c) Which type of error would the shop's owner consider more serious? d) Which type of error might environmentalists consider more serious?
a) The regulators decide that the shop is not meeting the standards when the shop is actually meeting them. b) The regulators certify that the shop is meeting the standards when the shop is not actually meeting them. c) Type I d) Type II
According to a recent poll, 25% of adults in a certain area have high levels of cholesterol. They report that such elevated levels "could be financially devastating to the regions healthcare system" and are a major concern to health insurance providers. According to recent studies, cholesterol levels in healthy adults from the area average about 209 mg/dL, with a standard deviation of about 35 mg/dL, and are roughly Normally distributed. Assume that the standard deviation of the recent studies is accurate enough to be used as the population standard deviation. If the cholesterol levels of a sample of 44 healthy adults from the region is taken, answer parts a through d. a) What shape will the sampling distribution of the mean have? b) What is the mean of the sampling distribution? c) What is the standard deviation? d) If the sample size were increased to 120, how would your answers to parts a-c change?
a) The sampling distribution of the mean is normal b) 209 c) 5.28 d) For part a, the shape of the distribution would also be normally distributed. For part b, the mean of the sampling distribution would remain as μ=209 mg/dL. For part c, the standard deviation of the sampling distribution would change to SD(y)=3.20 mg/dL
Suppose that you are testing the hypotheses H0: μ=89 vs. HA: μ≠89. A sample of size 31 results in a sample mean of 84 and a sample standard deviation of 1.8. a) What is the standard error of the mean? b) What is the critical value of t* for a 95% confidence interval? c) Construct a 95% confidence interval for μ. d) Based on the confidence interval, at α=0.050 can you reject H0? Explain.
a) The standard error of the mean is 0.3233. b) The critical value is t*=2.042 c) The 95% confidence interval for μ is (83.34, 84.66) d) Since the hypothesized mean 89 is greater than the values contained in the confidence interval, reject H0.
From a survey of coworkers you find that 47% of 250 have already received this year's flu vaccine. An approximate 95% confidence interval is (0.407,0.533). Which of the following are true? If not, explain briefly. a) 95% of the coworkers fall in the interval (0.407,0.533). b) We are 95% confident that the proportion of coworkers who have received this year's flu vaccine is between 40.7% and 53.3%. c) There is a 95% chance that a randomly selected coworker has received the vaccine. d) There is a 47% chance that a randomly selected coworker has received the vaccine. e) We are 95% confident that between 40.7% and 53.3% of the samples will have a proportion near 47%.
a) The statement is false. This doesn't make sense because workers are not proportions. b) The statement is true. c) The statement is false. There is not enough information to make an absolute statement about the population value with certainty. d) The statement is false. There is not enough information to make an absolute statement about the population value with certainty. e) The statement is false. The statement should be about the true proportion, not future samples.
For each of the following situations, state whether a Type I, a Type II, or neither error has been made. a) A test of H0: p=0.7 vs. HA: p<0.7 fails to reject the null hypothesis. Later it is discovered that p=0.6. b) A test of H0: μ=25 vs. HA: μ>25 rejects the null hypothesis. Later it is discovered that μ=24.9. c) A test of H0: p=0.6 vs. HA: p<0.6 fails to reject the null hypothesis. Later it is discovered that p=0.7. d) A test of H0: p=0.5 vs. HA: p≠0.5 rejects the null hypothesis. Later it is discovered that p=0.65.
a) Type II - Null should have been rejected b) Type I - Null should not have been rejected c) No error d) No error
Your company administers an executive aptitude test. They report test grades as z-scores, and you got a score of 1.70. They will admit to the executive training program only people who score in the top 19% on this test. a) With your z-score of 1.70, did you make the cut? b) What do you need to assume about test scores to find your answer in part a? A. No assumptions need to be made. B. The distribution of the test scores is bimodal. C. The distribution of the test scores is symmetric. D. The distribution of the test scores is unimodal. E. The distribution of the test scores is uniform.
a) With your z-score of 1.70, you do qualify for the executive training program. b) The distribution of the test scores is symmetric. The distribution of the test scores is unimodal.
Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true? a) For a given sample size, higher confidence means a smaller margin of error. b) For a specified confidence level, larger samples provide smaller margins of error. c) For a fixed margin of error, larger samples provide greater confidence. d) For a given confidence level, halving the margin of error requires a sample size twice as large.
false true true false
The probability of observing a particular value of a continuous random variable _______.
is 0
The histogram shows the ages (in years) of 25 customers that were in the freezer aisle at a large grocery store. Check the assumptions and conditions for an inference using Student's t-model Which assumptions and conditions are satisfied by the sample? The Independence Assumption _________ satisfied. The Randomization Condition _________ satisfied. The 10% Condition _________ satisfied. The Nearly Normal Condition _________ satisfied.
is not is not is is
Which of the following assumptions and conditions must be met to find a 95% confidence interval for a population proportion? Select all that apply. n < 10% of population size Sample size condition: np & nq > 10 Independence Assumption Sample size condition: n > 30 Random sampling
n < 10% of population size Sample size condition: np & nq > 10 Independence Assumption Random sampling
You take a random sample of size 36 from a normal population and find y-bar = 90 with a standard deviation = 24. When you test Ho: μ = 95 vs Ha: μ ≠ 95, what type of model will you use for the test? z-model t-model with 36 degrees of freedom t-model with 35 degrees of freedom
t-model with 35 degrees of freedom
A professor wondered if there was a difference in the proportion of students who dropped math classes between females and males. The professor randomly selected 20 math classes around campus and recorded the gender of the individual and whether or not a student enrolled in the class at the beginning of the term dropped the class at some point during the term. Assuming all conditions are satisfied, which of the following tests should the researcher use? one-sample z-test for proportions paired t-test Chi-square goodness of fit test two-sample t-test two-sample z-test for proportions
two-sample z-test for proportions
