Toegepaste Statistiek 1 (FEB11005)

A sample of 25 families were asked how many pets they owned. Their responses are
summarized in the following table.
Number of Pets 0 1 2 3 4 5
Number of Families 3 10 5 4 2 1
With respect to this sample we have:
The mean number of pets owned per family is

To compare starting salaries of male and female college graduates who find jobs, pairs are formed by choosing a male and a female with the same major and a similar grade point average (GPA). You can find the data in the table below.

The sample standard deviation for the 10 males was 11,665.15, for the women it was 11,616.95 and for the difference (Male – Female) it was 434.61

Morgan thinks that the weekly incomes are normally distributed and decides to construct a 95% confidence interval for the mean difference μD�� ( =μmale=����� - μFemale)�������).

Sally thinks that the prices of single family homes in the Netherlands differ with respect to the different provinces. To test whether this is indeed true she acquires samples of single family houses that were sold during the last three months in Friesland and Zuid-Holland. The results of these samples are collected in the table below:

Sally formulates the following hypotheses to determine if there is a difference in house prices:

H0: μA=μB vs. Ha: μA≠μB

where μA denotes the mean price of a single family home in Friesland, and μB denotes the mean price of a single family home in Zuid-Holland. Assuming that prices are normally distributed and that the population variances for the two provinces are equivalent, Sally carries out the appropriate t-test. She uses as significance level α=0.05

What is the absolute value of the appropriate test statistic used by Sally, rounded to two decimals accuracy?

(Based on a true story/experiment; the numbers are made up).

The German brand “Atheist” shoes received complaints from US customers concerning the delivery of shoes. According to some customers, delivery was unusually slow. It was suggested that this was related to the brand name (which was clearly printed on the parcels). To test this claim, the company decided to send out 40 boxes to 20 different addresses in the US. Of these 40 boxes, 20 were labeled as before, whereas the remaining 20 had no mention of the brand name on the box. The resulting pairs of boxes (one labeled, one unlabeled) were sent at the exact same time from the same post-office in Berlin. The addressees in the US were asked to report the arrival of the different boxes.

The results were as follows: For 5 shipments, the boxes took equally long to arrive; 3 of the “normal” (labeled) boxes arrived before the unlabeled ones; 12 unlabeled boxes arrived before the labeled ones.

Günter decides to use a sign test to test the hypothesis that there is no difference in the delivery times. That is:

H0:p=0.5 and Ha:p≠0.5

where p is the proportion of labeled boxes arriving before the unlabeled boxes.

What is the p-value obtained for the corresponding sign test, rounded to four decimals?

(Based on a true story/experiment; the numbers are made up).

The German brand “Atheist” shoes received complaints from US customers concerning the delivery of shoes. According to some customers, delivery was unusually slow. It was suggested that this was related to the brand name (which was clearly printed on the parcels). To test this claim, the company decided to send out 4040 boxes to 2020 different addresses in the US. Of these 4040 boxes, 2020 were labeled as before, whereas the remaining 2020 had no mention of the brand name on the box. The resulting pairs of boxes (one labeled, one unlabeled) were sent at the exact same time from the same post-office in Berlin. The addressees in the US were asked to report the arrival of the different boxes.

The results were as follows: For 55 shipments, the boxes took equally long to arrive; 33 of the “normal” (labeled) boxes arrived before the unlabeled ones; 1212 unlabeled boxes arrived before the labeled ones.

Günter decides to use a sign test to test the hypothesis that there is no difference in the delivery times. That is:

H0:p=0.5�0:�=0.5 and Ha:p≠0.5��:�≠0.5,

where p� is the proportion of labeled boxes arriving before the unlabeled boxes.

What is the p-value obtained for the corresponding sign test, rounded to four decimals?

To compare starting salaries of male and female college graduates who find jobs, pairs are formed by choosing a male and a female with the same major and a similar grade point average (GPA). You can find the data in the table below.

The sample standard deviation for the 1010 males was 11,665.1511,665.15, for the women it was 11,616.9511,616.95 and for the difference (Male – Female) it was 434.61434.61.

Morgan thinks that the weekly incomes are normally distributed and decides to construct a 9595% confidence interval for the mean difference μD�� ( =μmale=����� - μFemale)�������).

Morgan’s confidence interval is, rounded to two decimals: [_,_ ].