Question

A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the 0.08 significance level.
H0 : μ1 ≤ μ2
H1 : μ1 > μ2

a. Is this a one-tailed or a two-tailed test?
b. State the decision rule.
c. Compute the value of the test statistic.
d. What is your decision regarding H0?
e. What is the p-value?

Answer 1

Answer:

Step-by-step explanation:

The null hypothesis is

H0 : μ1 ≤ μ2

The alternative hypothesis is

H1 : μ1 > μ2

a) it is a one-tailed and also a right tailed test

b) The decision rule is the basis on which the null hypothesis is rejected or not. If 0.08 > p value, reject H0. If 0.08 < p value, do not reject H0.

c) Since the population standard deviations are known, we would use the formula to determine the test statistic(z score)

z = (x1 - x2)/√σ1²/n1 + σ2²/n2

Where

x1 and x2 represents sample means

σ1 and σ2 represents population standard deviations

n1 and n2 represents number of samples

From the information given,

x1 = 2.67

x2 = 2.59

σ1 = 0.75

σ2 = 0.66

n1 = 65

n2 = 50

z = (2.67 - 2.59)/√0.75²/65 + 0.66²/50

= 0.08/√0.00865 + 0.008712

z = 0.61

From the normal distribution table, the probability value corresponding to the z score is 0.73

d) If 0.08 > 0.73, we would reject H0

e) the p-value is 0.73