F25In 201347%indicated that 31of business owners gave a holiday gift to their employees. A 2014 survey of 33 business owners% plan to provide a holiday gift to their employees. Is there reason to believe the proportion,of business owners providing gifts has decreased at a-0.005? (See exercise 40 on page 418 of your textbookfor a similar problem.)For the hypothesis stated above...Question 1What is/are the critical value(s)?Question 2What is the test statistic?Question 3What is the conclusion?

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Step 1

a.

The conditions for the proportion test for sample size n and the true population proportion p,

• The data should be selected randomly.
• Product np is greater than or equal to 10
• Product n(1–p) is greater than or equal to 10

Let p be the proportion of business owners gave a holiday gift to their employees.

Conditions for this problem:

Here 33 business owners were selected randomly.

For this problem,

Step 2

Hence, the conditions satisfied.

For the given problem, we should use one sample proportion z-test.

Let p be the proportion of business owners gave a holiday gift to their employees.

The aim is to check whether the proportion of proportion of business owners providing gifts has decreased or not.

It is given that in 2013, 47% of business owners gave a holiday gift to their employees.

The null and the alternative hypothesis is,

Step 3

Here the level of significance is 0.005.

Decision based on the critical-value method:

• If z ≤ –zα, then reject.

From the EXCEL, using the formu...

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