Problem 1: A random sample obtained from a population with variance =400, and

sample mean is computed to be . Consider the null hypothesis and

alternative hypothesis . Compute the critical value and state your decision

rule for the following options regarding sample size:

a) n=25 (b) n=16, (c) n=44

Also calculate 95% confidence interval for each of the case and make your decision rule

Problem 2: The weekly salary of all customer service workers of a company has had

mean of $400 with standard deviation $48.6. In contract negotiation, the company claims

that a new incentive scheme has increased the average weekly earnings for all workers.

A union representation takes a random sample of 15 workers and finds that their weekly

earning have an average of $421.35.

(a) Test the company claims at 5% level of significance. Sketch the distribution of

test statistic under null and alternative hypothesis showing rejection region.

(b) Find 95% CI for the population mean of weekly salary and P-values. Based on CI

and P-value, would you able to have same conclusion that obtained in (a)?

Problem 3: A telephone company claims that the mean duration of all long-distance

phone calls made by its residential customers is 10 min- Utes. A random sample of 25

long-distance calls made by its residential customers taken from the records of this

company showed that the mean duration of calls for this sample is 9.20 minutes with

standard deviation of 2.80 minutes. Using these sample information, investigate the

company's claims at 1% level of significance. Find the p-value and interpret it.

Problem 4: Prior to joining a coaching course, a netball player has scored with 45% of

her shots at the basket, and so is considered to have a scoring ability of 0.45. In games

following the course, she scores with 72 of her 135 shots at the basket. Stating clearly any

assumptions made, investigate whether or not the course has improved her shooting

ability. Use 5% level of significance.

Problem 5: Junior school research team would like to examine whether students

performance in math is increased after recruiting two high qualified math teachers. Both

pre-test and post-test scores of a random sample of 20 students was recoded. The mean

difference between posttest and pre-test score was 15.4 with standard deviation 3.4. Does

the data provide evidence to conclude that students performance in math is increased. Use

5% level of significance. Find 95% CI for the true difference and make conclusion on

hypothesis.

.

Problem 6: An educational study was designed to investigate the effectiveness of a

reading program of elementary age children. Each child was given a pre-test and post2

s

x = 70 Ho : = 80

: 80 H1

population, a random sample of scores of pre-test and post test are as follows:

Child: 1 2 3 4 5 6 7

Pre-test: 40 36 32 38 32 33 35

Post-test: 48 42 36 37 43 38 45

(a) Test whether the program is effective at 5% level of significance. State the

necessary assumptions

b) Find 90% CI for the difference of the population means of scores. Based on CI,

would you able to have same conclusion that obtained in (a)?

c) Find p-value and interpret it

Problem 7: The communication minister wanted to know if there is difference between

the traffic speeding fines paid by the residents of Dhaka (DHK) and the residents of

Chittagong city (CTG). The independent random samples of the amount of fines paid by

the residents in each of the two cities are given below:

DHK : 100 125 135 128 140 142 128 137 156 142

CTG: 95 87 100 75 110 105 85 95 - -

(a) Test the minister claims at 5% level of significance. State necessary assumptions

(b) Find 90% CI for the difference between two population means of fines paid by the

residents. Based on CI, would you able to have same conclusion that obtained in

(a)?