Question

Scenario: A corporation randomly selects 150 sales people and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 sales people wanted a self-improvement course. The groups are assumed to be independent random samples. Let straight pi subscript 1 space and space straight pi subscript 2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study respectively. What is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions using alpha equals 0.10

Answer 1

Answer:

The calculated Z = 1.2 < 1.645 at  0.1 level of significance

Null hypothesis is accepted

There is a no difference in the two population proportions using alpha equals 0.10

Step-by-step explanation:

Given first sample size n₁ = 150

Given first sample proportion p₁ =  0.66

Given second sample size n₂ = 160

Given second sample proportion p₂ =  0.60

Null hypothesis :H₀: p₁ =  p₂

Alternative Hypothesis: H₁:p₁ ≠  p₂

Test statistic

$Z = \frac{p_{1} - p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }$

Where

$P =\frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1} +n_{2} } = \frac{150 X 0.66+160 X0.60}{150+160} = 0.629$

Q = 1- P = 1- 0.629 = 0.371

$Z = \frac{0.66 - 0.60 }{\sqrt{0.629 X0.371(\frac{1}{150 }+\frac{1}{160} ) } }$

Z = 1.2

Level of significance  ∝=0.1

The critical value at ∝=0.1

$Z_{0.10} = 1.645$

The calculated Z = 1.2 < 1.645 at  0.1 level of significance

Null hypothesis is accepted

There is a no difference in the two population proportions using alpha equals 0.10