Exercises. 1. The following information was obtained from two independent samples selected from two normally distributed populations with unknown but equal variances

1. The following information was obtained from two independent samples selected from two normally distributed populations with unknown but equal variances

; ; ;

; ;

a) Test at 1% significance level if the two population means are different.

b) Test at 5% significance level if is different than .

2. The following summary statistics are recorded for independent random samples from two normally distributed populations with equal variances

Sample 1Sample 2

Test the null hypothesis against the alternative that with .

3. Salary surveys of marketing and management majors show the following starting annual salary data

Marketing majorsmanagement majors

Consider the test of the hypothesis that the mean annual salaries are the same for both majors. For can you conclude that a difference exists in the mean annual salary for the two majors?

4. A professor took two samples, one of 21 males and another of 15 females from university students who were enrolled in business statistics at the same university. He found that the mean score of male students in a mid-term examination in statistics was 75.3 with a standard deviation of 6.4, and the mean score of female students was 78.3 with a standard deviation of 7.3. Assume that the scores of all male and all female students are normally distributed with equal but unknown standard deviations.

Test at the 2.5 significance level if the mean score in business statistics for all male and female students are the same against the alternative that male students have lower score than that for all female students.

5. The management of a supermarket wanted to investigate if the male customers spend less money on average, than the female customers. A sample of 16 male customers who shopped at this supermarket showed that they spent an average of $55 with a standard deviation of $12.50. Another sample of 22 female customers who shopped at the supermarket showed that they spent an average of $63 with a standard deviation of $14.5. Assume that the amounts of money spent at this supermarket by all male and female customers are normally distributed with equal but unknown population variance. Test at the 5% significance level if the mean amount spent by all male and female customers are the same against the alternative that male customers at this supermarket spend less than that of female customers.

6. A bank has two branches. The quality department wanted to check if the customers are equally satisfied with the service provided at these two branches. Randomly selected customers asked to measure the satisfaction of services (on scale of 1 to 11, 1 being the lowest and 11 being the highest).

A random sample of six customers from the branch A produced following data:

9.50; 8.60; 8.59; 6.50; 4.79; 4.29

An independent random sample of six customers selected from the branch B produced following data:

10.21; 9.66; 7.67; 5.12; 4.88; 3.12

Stating any assumptions you need to make, test against two sided alternative the null hypothesis that the two populations mean satisfaction index for all customers for the two branches are the same.

7. Given that , , , and , ,

. Test against with .

8. A researcher wants to test the mean GPA (grade point averages) of all male and all female university students. She took a random sample of 28 male students and 24 female students. She found that GPA’s of the two groups to be 2.62 and 2.74, respectively, with the corresponding standard deviations equal to 0.43 and 0.38. Test at the 5% significance level if the mean GPA’s of the two populations are equal against two sided alternative.

Assume that the GPA’s of all male and female students are normally distributed with equal but unknown standard deviations.

Дата добавления: 2015-08-05