# Hypothesis testing and confidence interval

Dear Ota,

Provide me the solution with explanation.

Thanks

1.

A 95% confidence interval (a t interval) for the lives (in minutes) of Kodak AA batteries is 440 < u < 480. Assume that this result is based on a sample of size 25.

1a. What is the value of the sample mean?

a. 455

b. 440

c. 445

d. 460

e. 470

2.

1b. What is the value of the sample standard deviation?

a. 363.43

b. 181.71

c. 36.3 2

d. 48.45

3.

1c. Construct the 99% confidence interval.

a. (433.0, 487.1)

b. (442.6, 467.4)

c. (440.0, 470.0)

d. (434.7, 475.3)

4.

1d. If the confidence interval 443.4 < u < 476.6 is obtained from the same

sample data, what is the degree of confidence?

a. 80%

b. 85%

c. 90%

d. 95%

5.

David wants to rent an unfurnished apartment for next semester.

He took a random sample of 9 apartments adversised in the local

Halifax paper, and recorded the rental rates. The rents (in $

per month) were:

500 650 600 505 450 550 515 495 640

2a) Find a 90% confidence interval for the mean monthly rent for

unfurnished apartments in this this community.

a. (384,706)

b. (408,682)

c. (491,599)

d. (502,588)

6.

2b) You wish to test the null hypothesis that the true mean monthly rent for an unfurnished apartment is $500. What is the value of the test statistic?

a. .028

b. .64

c. 1.82

d. 1.93

7.

2c) A student at the University of Calgary carried out a similar study, but using a sample of 16 apartments. The value of the test statistic for that study was 2.71. What would be the p-value to test against the alternative that the mean rent is not equal to $500.

a. p < .005

b. .005 < p < .01

c. .01 < p < .02

d. .02 < p < .04

e. .04 < p < .05

f. .05 < p < .1

g. .1 < p

8.

Consider the following independent measurements taken from a normal population:

12,10,7,13,9,10,11,7,9

3a. What is the standard error of the sample mean?

a. 2.048

b. 0.228

c. 0.382

d. 0.683

e. 4.194

9.

Question 3b. Find a 95% confidence interval for the population mean.

a. (7.487, 12.069)

b. (8.019, 11.537)

c. (8.060, 11.495)

d. (8.204, 11.352)

e. (8.508, 11.047)

10.

A school board is evaluating a learning system designed to increase literacy skills. A standardized test measuring reading skills is performed to some students, both before and after using the learning system. The following data were obtained:

student before after difference

1 96 96 0

2 101 105 4

3 108 112 4

4 97 96 -1

5 108 114 6

6 93 97 4

7 95 100 5

8 91 92 1

9 114 113 -1

Is there evidence that the learning system has increased the test scores?

4a) What is the null hypothesis?

a. mu = 0

b. mu < 0

c. mu > 0

d. mu not equal to 0

11.

4b) What is the alternative hypothesis?

a. mu = 0

b. mu < 0

c. mu > 0

d. mu not equal to 0

12.

4c) How may degrees of freedom are there?

a. 18

b. 16

c. 9

d. 8

13.

4d) What is the sample standard deviation of the difference in the test scores?

a. 7.73

b. 2.70

c. 2.45

d. 6.00

14.

4e) What is the value of the test statistic?

a. between 0 and 1

b. between 1 and 3

c. between 3 and 5

d. between 5 and 10

e. more than 10

15.

4f) What is the p-value?

a. between 0 and 0.01

b. between 0.01 and 0.05

c. between 0.05 and 0.1

d. between 0.1 and 0.25

e. more than 0.25

16.

4g) Is there evidence of a increase in the test scores at significance level alpha = 0.05?

a. yes

b. no

c. not enough information

#### Solution Summary

Step by step method for testing the hypothesis under 5 step approach is discussed here. Excel template for each problem is also included. This template can be used to obtain the answers of similar problems.