Question

In a survey of 155 senior​ executives, 51​% said that the most common job interview mistake is to have little or no knowledge of the company. Use a 0.01 significance level to test the claim that in the population of all senior​executives, 40​% say that the most common job interview mistake is to have little or no knowledge of the company. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution. Identify the null and alternative hypotheses.

The test statistic is ​(Round to two decimal places as​ needed.)

The​ P-value is ​(Round to four decimal places as​ needed.)

Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim.

reject/ fail to reject H0 because There is not / is sufficient evidence to warrant rejection of the claim that among senior​ executives, 40​% say that the most common job interview mistake is to have little or no knowledge of the company.

Answer 1

Let p be the true proportion of senior​executives, who say that the most common job interview mistake is to have little or no knowledge of the company

The claim is the 40​% of senior​executives say that the most common job interview mistake is to have little or no knowledge of the company, that is p=0.40

Identify the null and alternative hypotheses.

ans: The hypotheses are

Use a 0.01 significance level to test the claim

The level of significance is

From the sample we have the following

n=155 is the sample size

is the sample proportion of senior​executives, who say that the most common job interview mistake is to have little or no knowledge of the company

is the hypothesized value of the proportion

The standard error of proportion is

Since are both greater than 5, we can use normal distribution as the sampling distribution of proportions.

The test statistic is ​(Round to two decimal places as​ needed.)

ans: The test statistic is 2.80

The​ P-value is ​(Round to four decimal places as​ needed.)

This is a 2 tailed test (the alternative hypothesis has "not equal to")

The p-value is

ans: The p-value is 0.0052

Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim.

We will reject the null hypothesis if the p-value is less than the significance level.

Here, the p-value is 0.0052 and it is less than the significance level alpha=0.01. Hence we reject the null hypothesis.

ans: reject H0 because the p-value is less than

There is sufficient evidence to warrant rejection of the claim that among senior​ executives, 40​% say that the most common job interview mistake is to have little or no knowledge of the company.