Question

In 2013, 43% of business owners gave a holiday gift to their employees. A 2014 survey of 53 business owners indicated that 31% plan to provide a holiday gift to their employees. Is there reason to believe the proportion of business owners providing gifts has decreased at α=0.025?

1. What is/are the critical values?

2. What is the test statistic?

3. What is the conclusion? tinsetc/tisetc (four decimal places)

Answer 1

Let p be the population proportion of business owners gave a holiday gift to their employees in 2014.

In a random sample of of 53 business owners indicated that 31% plan to provide a holiday gift to their employees.

i.e n=53

and

at 2.5% level of significance we want to test the claim that the proportion of business owners providing gifts has decreased from 2013's proportion of 0.43

a) The hypothesis testing problem is:

The critical value at 2.5% level of significance for upper tail test is:

### By using z table:

b) The test statistic is:

3) Since -1.76>-1.96, we are unable to reject the null hypothesis at 2.5% level of significance.

Therefore we do not have sufficient evidence to believe the proportion of business owners providing gifts has decreased at α=0.025