Question

The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion exceeds 30%, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 75 have PC's at home. Find the rejection region for this test using a = .05

- reject h is z is greater than 1.645




reject h is z= 1.645




reject h if z is less than -1.645




reject h if z is greater than 1.96 or z is less than -1.96

Answer 1

The rejection region for the given hypothesis test with a significance level of 0.05 is when the z-score is greater than 1.645.

Step-by-step explanation:

To find the rejection region for this hypothesis test, we need to use the given significance level (alpha, a) of 0.05 to determine the critical z-value. In a one-tailed test, because we are looking for the proportion that exceeds 30%, we focus on the right tail of the normal distribution. Referencing the normal distribution table, a z-value with 0.05 to its right is approximately 1.645. Hence, we reject the null hypothesis if our test statistic z is greater than 1.645.

Utilizing the sample data where 75 out of 250 business students have PCs at home, we would calculate the test statistic and compare it to the critical value. If our calculated z-score exceeds 1.645, then we would reject the null hypothesis and conclude that more than 30% of business students have PCs at home, leading the lab to reconsider its proposed expansion.

Answer 2

Option A) reject null hypothesis if z is greater than 1.645

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 250

p = 30% = 0.3

Alpha, α = 0.05

Number of women belonging to union , x = 75

First, we design the null and the alternate hypothesis

`H_(0): p = 0.3\\H_A: p > 0.3`

This is a one-tailed(right) test.

Rejection Region:

`z_(critical) \text{ at 0.05 level of significance } = 1.645`

So, the rejection region will be

`z > 1.64`

That is we will reject the null hypothesis if the calculated z-statistic is greater than 1.645

Option A) reject null hypothesis if z is greater than 1.645