Reference no: EM13371298
1. Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Time Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex television commercials. Let p represent the true proportion of consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of .05 or less at a 99% confidence level?
A) 550
B) 600
C) 650
D) 700
E) 750
2. A telephone poll of an SRS of 1234 adults found that 62% are generally satisfied with their lives. The announced margin of error for the poll was 3%. Does the margin of error account for the fact that some adults do not have telephones?
A) Yes. The margin of error includes all sources of error in the poll.
B) Yes. Taking an SRS eliminates any possible bias in estimating the population proportion
C) Yes. The margin of error includes undercoverage but not nonresponse.
D) No. The margin of error includes nonresponse but not undercoverage.
E) No. The margin of error only includes sampling variability.
3. A Census Bureau report on the income of Americans says that with 90% confidence the median income of all U.S. households in a recent year was $57,005 with a margin of error of +/- $ 742. This means that
A) 90% of all households had incomes in the range $57,005 +/- $742
B) We can be sure that the median income for all house-holds in the country lies in the rage $57,005 +/- $742
C) 90% of the households in the sample interviewed by the Census Bureau had incomes in the range $57,005 +/- 742
D) The Census Bureau got the result $57,005 +/- $742 using a method that will cover the true median income 90% of the time when used repeatedly.
E) 90% of all possible samples of this same size would result in the sample median that falls within $742 of $57,005
4. A random sample of 100 likely voters in a small city produced 59 voters in favor of candidate A. The observed value of the test statistic for testing the null hypothesis H0 : p = .5 versus the alternative hypothesis Ha : > 0.5 is
5. An SRS of 100 postal employees found that the average time these employees had worked at the postal service was 7 years with standard deviation 2 years. Do these data provide convincing evidence that the mean time of employment µ for the population of postal employees has changed from the value of 7.5 that was true 20 years ago?
To determine this, we test the hypothesis versus using a one sample t test. What conclusion should we draw at the 5% significance level?
A) There is convincing evidence that the mean time working with the postal service has changed.
B) There is not convincing evidence that the mean time working with the postal service has changed.
C) There is convincing evidence that the mean time working with the postal service is still 7.5 years.
D) There is convincing that the mean time working with the postal service is now 7 years.
E) We cannot draw a conclusion at the 5% significance level. The sample size is too small.
6. Are TV commercials louder than their surrounding programs? To find out, researchers collected data on 50 randomly selected commercials in a given week. With the television's volume at a fixed setting, they measured the maximum loudness of each commercial and the maximum loudness in the first 30 seconds of regular programming that followed. Assuming conditions for inference are me, the most appropriate method for answering the question of interest is
a) a one-proportion z test
b) a one-proportion z interval
c) a paired t test
d) a paired t interval
e) none of these
7. A study of road rage asked separate random sample of 596 men and 523 women about their behavior while driving. Based on their answers, each respondent was assigned a road rage score on a scale of 0 to 20. Are the conditions for performing a two-sample t test satisfied?
A) Maybe; we have independent random samples, but we need to look at the data to check normality.
B) No; road rage scores in a range between 0 and 20 can't be normal.
C) No; we don't know the population standard deviations
D) Yes; the large sample sizes guarantee that the corresponding population distributions will be Normal.
E) Yes; we have two independent random samples and large sample sizes.
8. A quiz question gives random samples of n=10 observations from each two normal distributed populations. Tom uses a table of t distribution critical values and 9 degrees of freedom to calculate a 95% confidence interval for the difference in the two population means. Janelle uses her calculator's two sample t interval with 16.87 degrees of freedom to compute the 95% confidence interval. Assume that both students calculate the intervals correctly. Which of the following is true?
A) Tom's confidence interval is wider
B) Janelle's confidence interval is wider
C) Both confidence intervals are the same
D) There is insufficient information to determine which confidence interval is wider.
E) Janelle made a mistake; degrees of freedom has to be a whole number.
A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be 6 hours with a standard deviation of 3 hours. The researchers also obtained an independent SRS of 40 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be 5 hours with a standard deviation of 2 hours. Suppose that the researcher decides to carry out a significance test of H0: υsuburban = υcity versus a two-sided alternative.
9. The p value for the test is 0.048. A correct conclusion is to
A) Fail to reject H0 at the α = 0.05 level. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
B) Fail to reject H0 at the α = 0.05 level. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
C) Fail to reject H0 at the α = 0.05 level. There is convincing evidence that the average time spent on extracurricular activities by students in the suburban and city school districts is the same.
D) Reject H0 at the α = 0.05 level. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts
E) Reject H0 at the α = 0.05 level. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
10. At a baseball game, 42 of 65 randomly selected people report owning an iPod. At a rock concert occurring at the same time across town, 34 of 52 randomly selected people report owning an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90% confidence interval for the difference in population proportions is (-0.154, 0.138). Which of the following gives the correct outcome of the researcher's test of the claim?
A) Since the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is the same.
B) Since the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is different.
C) Since the confidence interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different.
D) Since the confidence interval includes more negative than positive values, the researcher can conclude that a higher proportion of people at the rock concert own ipods than at the baseball game.
E) The researcher cannot draw a conclusion about a claim without performing a significance test.
11. How much more effective is exercise and drug treatment than drug treatment alone at reducing the rate of heart attacks among men aged 65 and older? To find out, researchers perform a completely randomized experiment involving 1000 healthy males in this age group. Half of the subjects are assigned to receive drug treatment only. While the other half are assigned to exercise regularly and to receive drug treatment. The most appropriate inference method for answering the original research question is
A) one sample z test for a proportion
B) two sample z interval for p1-p2
C) two sample z test for p1-p2
D) two sample t interval for u1-u2
E) two sample t test for u1-u2
FREE RESPONSE:
1) Does drying barley seeds in a kiln increase the yield of barley? A famous experiment by William S. Gosset (who discovered the t distributions) investigated this question. Eleven pairs of adjacent plots were marker out in a large field. For each pair, regular barley seeds were planted in one plot and kiln-dried seeds were planted in the other. The following table displays the data on yield (lb/acre).
|
Plot
|
Regular
|
Kiln
|
|
1
|
1903
|
2009
|
|
2
|
1935
|
1915
|
|
3
|
1910
|
2011
|
|
4
|
2496
|
2465
|
|
5
|
2108
|
2180
|
|
6
|
1961
|
1925
|
|
7
|
2060
|
2122
|
|
8
|
1444
|
1482
|
|
9
|
1612
|
1542
|
|
10
|
1316
|
1443
|
|
11
|
1511
|
1535
|
12 A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $100 for the upgrade. For the upgrade to be profitable, the company needs to sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay $100 for the upgrade.
(a) Do the sample data give good evidence that more than 20% of the company's customers are willing to purchase the upgrade? Carry out an appropriate test at the significance level.
(b) Describe a Type I and a Type II error in the context of this problem. Which would be the more serious mistake in this setting and why?
13. "I can't get through my day without coffee" is a common statement from many students. Assumed benefits include keeping students awake during lectures and making them mote alert for exams and tests. Students in a statistics class designed an experiment to measure memory retention with and without drinking a cup of coffee one hour before a test. This experiment took place on two different days in the same week (Monday and Wednesday). Ten students were used. Each student received no coffee or one cup of coffee, one hour before the test on a particular day. The test consisted of a series of words flashing on a screen, after which the student had to write down as many of the words as possible. On the other day, each student received a different amount of coffee (none or one cup).
(a) The data from the experiment are provided in the table below. Set up and carry out an appropriate test to determine whether ther is convincing evidence that drinking coffee improves memory.
|
Student
|
No cup
|
One cup
|
|
1
2
3
4
5
6
7
8
9
10
|
24
30
22
24
26
23
26
20
27
28
|
25
31
23
24
27
25
28
20
27
30
|
14. Pat wants to compare the cost of one and two-bedroom apartments in the area of her college campus.She collects data for a random sample of 10 advertisements of each type. Here are the rents (in dollars per month):
One-bedroom: 500 650 600 505 450 550 515 495 650 395
Two-bedroom: 595 500 580 650 675 675 750 500 495 670
Pat wonders if two-bedroom apartments rent for significantly more, on average, than one-bedroom apartments. She decides to perform a test of H0: u1=u2 versus Ha:u1<u2 where u1 and u2 are the true mean rents for all one-bedroom and two bedroom apartments, respectively, near campus.
A) Name the appropriate test and show that the conditions for carrying out this test are met.
B) The appropriate test from part a yields a P-value of 0.058. Interpret this P-value in context
C) What conclusion should Pat draw at the α = 0.05 significance level? Explain.
15. A random sample of 100 of a certain popular car model last year found that 20 had a certain minor defect in the brakes. The car company made an adjustment in the production process to try to reduce the proportion of cars with the brake problem. A random sample of 350 of this year's model found that 50 had the minor brake defect.
A) Was the company's adjustment successful? Carry out an appropriate test to support your answers.
B) Describe a Type I error and a Type II error in this setting and give a possible consequence for each