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Exam 10: Two-Sample Hypothesis Tests

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Question 1

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A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies.She weighed a random sample of five babies of each gender.Their weights (pounds) are shown below,along with some MegaStat results. The population means:

A) may be assumed equal at any customary .
B) should be assumed unequal at any customary .
C) are not relevant to this paired t-test.

D) None of the above
E) A) and C)

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Question 2

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In a random sample of patient records in Cutter Memorial Hospital,six-month postoperative exams were given in 90 out of 200 prostatectomy patients,while in Paymor Hospital such exams were given in 110 out of 200 cases.In comparing these two proportions,normality of the difference may be assumed because:

A) the populations are large enough to be assumed normal.
B) the probability of success can reasonably be assumed constant.
C) the samples are random,so the proportions are unbiased estimates.
D) n  10 and n(1 - )  10 for each sample taken separately.

E) None of the above
F) B) and D)

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Question 3

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An F-test for equality of variances gives a p-value of .003.At  = .05,what conclusion can be made about the preferred test to compare the means for the same sample?

A corporate analyst is testing whether mean inventory turnover has increased.Inventory turnover in six randomly chosen product distribution centers (PDCs) is shown. The right-tailed critical value at  = 0.005 is:

If the population variances are exactly equal,the sample F test statistic will be zero.

A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20,while 6 males had a mean of $17.30 with a standard deviation of $9.60.At  = .10,to test for equal variances in a two-tailed test,the critical values are:

Group 1 has a mean of 13.4 and group 2 has a mean of 15.2.Both populations are known to have a variance of 9.0 and each sample consists of 18 items.What is the test statistic to test for equality of population means?

The difference between two sample proportions p₁ - p₂ may be assumed normally distributed if each sample has at least 10 "successes" and 10 "failures."

Jason wants to perform a two-tailed test for equality between two independent sample proportions.Each sample has at least 10 "successes" and 10 "failures." Jason's test statistic is -1.44.What is his p-value?

Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the time to perform an appendectomy.A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes,while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes.For a right-tail test of equal means (assume equal variances) ,the pooled variance is:

The table below shows the mean number of daily errors by seven air traffic controller trainees during the first two weeks on the job.We want to perform a paired t-test at  = .05 to see if the mean daily errors have decreased from Week 1 to Week 2. The right-tailed critical value at  = 0.05 is:

Litter sizes (number of pups) for randomly chosen dogs from two breeds were compared.The sample data were entered into Excel,and the following results were produced. What is the p-value for a left-tailed test comparing the means at  = .05?

In a left-tailed test comparing two means with unknown variances assumed to be equal,the test statistic was t = -1.81 with sample sizes of n₁ = 8 and n₂ = 12.The p-value would be:

A paired t-test with two columns of 10 observations in each column would use d.f.= 18.

The table below shows the mean number of daily errors by air traffic controller trainees during the first two weeks on the job.We want to perform a paired t-test at  = .05 to see if the mean daily errors decreased significantly. The test statistic is:

The test statistic in an F test for equal variances is the ratio of the sample variances.

The coach of an adult Master's Swim class selected eight swimmers within each of the two age groups shown below.A 50-yard freestyle time is recorded for each swimmer.The resulting times (seconds) are shown below.Which statistical test would you choose to compare the two groups?

A new policy of "flex hours" is proposed.Random sampling showed that 28 of 50 female workers favored the change,while 22 of 50 male workers favored the change.Management wonders if there is a difference between the two groups.What is the p-value for a two-tailed test?

The table below shows two samples taken to compare the mean age of individuals who purchased the iPhone 3G at two AT&T store locations. What are the critical values for a two-tailed test for equal variances at  = .05?

The table below compares two samples taken to compare the mean age of individuals who purchased the iPhone 3G at two AT&T store locations.Very briefly,what conclusions can you draw?