Question

In 2013, 30% of business owners gave a holiday gift to their employees. A 2014 survey of 53 business owners indicated that 19% 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=0.05?

1)- What is/are the critical values?

2)- What is the test statistics?

3)- What is the conclusion?

Please explain in detail and step by step

Answer 1

Solution :

Given that,

= 0.30

1 - = 0.70

n = 53

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 0.19

This a left (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.30

Ha: p < 0.30

Step - 1

Critical value of  the significance level is α = 0.05, and the critical value for a two-tailed test is

= -1.645

Step - 2

Test statistics

z = ( - ) / *(1-) / n

= ( 0.19 - 0.30) / (0.30*0.70) / 53

= -1.768

Step - 3

Since it is observed that z = -1.768 < = -1.645 , it is then concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion of business owners providing gifts has decreased at a=0.05 significance level.