1. A sample of 50 observations is selected from one population with a population standard deviation of 4. The sample mean is 101. A sample of 54 observations is selected from a second population with a population standard deviation of 6. The sample mean is 98. Conduct the following test of hypothesis using the 0.02 significance level:

H₀ : ₁ - ₂ = 0

H_{1 : 1} - ₂ = 0

a) This is a two - tailed test.

b) State the decision rule. ( Negative answer should be indicated by a minus sign. Round the final answer to 2 decimal places.)

The decision rule is to reject H₀ if z is ------ the interval ( --------- , ------ )

c) Compute the value of the test statistics. (Round answer to 2 decimal places)

d) What is your decision regarding H₀ ?

e) What is the p-value?

2. The null and alternate hypotheses are:

H₀ : ₁ - ₂ = 0

H₁ : ₁ - ₂= 0

A random sample of 16 observations from the first population revealed a sample mean of 367 and a sample standard deviation of 10. A random sample of 17 observations from the second population revealed a sample mean of 362 and a sample standard deviation of 10.

At the 0.1 significance level, is there a difference in the population mean?

a) State the decision rule. ( Round the answer to 3 decimal places and negative answers indicate by minus sign)

The decision rule is to reject H₀ if t < ----- or > -------

b) Compute the pooled estimate of the population variance. ( round the final answer to 2 decimal places)

c) Compute the test statistic? ( round the final answer to 3 decimal places)

d) What is your decision regarding H₀?

e) Estimate the p-value?

3. The null and alternative hypothesis are:

H₀: _d = 0

H₁ : _d= 0

The following paired observations show the number of traffic citations given for speeding by Officer Dhondth and Officer Meredit of the Ontario Provincial Police (OOP) for the last five months :

	May	June	July	August	September
Officer Dhondth	35	17	28	22	34
Officer Meredit	27	16	15	18	30

At the 0.05 significance level, is there a difference in the mean number of citations given by the two officers?

a) State the decision rule. ( round the final answer to 3 decimal places and if the answer is negative insert minus sign )

Reject H₀ if t < ------ or t > ------

b) Compute the value of the test statistic. ( Negative answer indicate by a minus sign. And round the final answer to 3 decimal places)