Question

A study is done to test the claim that Company A retains its workers longer than Company B. Company A samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company B samples 21 workers, and their average time with the company is 4.6 years with a standard deviation of 0.9. The populations are normally distributed

Answer 1

Answer:-

Given that:-

A study is done to test the claim that Company A retains its workers longer than Company B. Company A samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company B samples 21 workers, and their average time with the company is 4.6 years with a standard deviation of 0.9. The populations are normally distributed

The provided sample means are shown below:

Also, the provided sample standard deviations are :

and the sample sizes are and

(1) Null and Alternative Hypothesis

The following null and alternative hypothesis need to be tested

This corresponds to a right - tailed test, for which a t - test for two population means , with two independent samples , with unknwon population standard deviation will be used.

(2) Rejection Region:

Based on the information provided ,the significance level is and the degrees of freedom are df =3.5 In fact ,the degrees of freedom are computed as follows ,assuming that the population variances are equal:

Hence, it is found that the critical value for this right - tailed is

(3) Test Statistics :

Since it is assumed that the population variances are equal, the t - Statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that it is is then concluded that the null hypothesis is rejected.

using the p - value approach : The p - value is p = 0.0383, and since p = 0.0383<0.05, it is concluded that the null hypothesis is rejected .

(5) Conclusion

It is concluded that the null hypothesis is rejected . Therefore , there is enough evuidence to claim that population mean is greater than at the 0.05 signioficance level .

Confidence interval

The 95% confidence interval is

Therefore, the claim is true that the company A retains its workers longer than company B.

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