A personnel manager claims that 80 per cent of all single women hiredf

1.	A personnel manager claims that 80 per cent of all single women hiredfor secretarial job get married and quit work within two years after they arehired. Test this hypothesis at 5% level of significance if among 200 suchsecretaries, 112 got married within two years after they were hired and quit theirjobs.
Answer» We conclude that percent of all single women hired for a secretarial job get married and quit work within two years after they are hired is different from 80%. Step-by-step explanation: We are given that a personnel MANAGER CLAIMS that 80% of all single women hired for a secretarial job get married and quit work within two years after they are hired. Also, among 200 such SECRETARIES, 112 GOT married within two years after they were hired and quit their jobs. Let p = population proportion of all single women hired for a secretarial job get married and quit work within two years after they are hired So, Null Hypothesis, $H_0$ : p = 80% {means that 80% of all single women hired for a secretarial job get married and quit work within two years after they are hired} Alternate Hypothesis, $H_A$ : p $\neq$ 80% {means that different from 80% of all single women hired for a secretarial job get married and quit work within two years after they are hired} The test statistics that will be used here is One-sample z-test for proportions; T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1) where, $\hat p$ = sample proportion of single women who were hired for a secretarial job get married and quit work within two years after they are hired = $\frac{112}{200}$ = 0.56 n = sample of secretaries = 200 So, the test statistics = $\frac{0.56-0.80}{\sqrt{\frac{0.80(1-0.80)}{200} } }$ = -8.485 The value of z-test statistics is -8.485. Now, at a 5% level of significance, the z table gives a critical value of -1.96 and 1.96 for the two-tailed test. Since the value of our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region. Therefore, we conclude that different from 80% of all single women hired for a secretarial job get married and quit work within two years after they are hired.

A personnel manager claims that 80 per cent of all single women hiredfor secretarial job get married and quit work within two years after they arehired. Test this hypothesis at 5% level of significance if among 200 suchsecretaries, 112 got married within two years after they were hired and quit theirjobs.

Answer»

We conclude that percent of all single women hired for a secretarial job get married and quit work within two years after they are hired is different from 80%.

Step-by-step explanation:

We are given that a personnel MANAGER CLAIMS that 80% of all single women hired for a secretarial job get married and quit work within two years after they are hired.

Also, among 200 such SECRETARIES, 112 GOT married within two years after they were hired and quit their jobs.

Let p = population proportion of all single women hired for a secretarial job get married and quit work within two years after they are hired

So, Null Hypothesis, $H_0$ : p = 80% {means that 80% of all single women hired for a secretarial job get married and quit work within two years after they are hired}

Alternate Hypothesis, $H_A$ : p $\neq$ 80% {means that different from 80% of all single women hired for a secretarial job get married and quit work within two years after they are hired}

The test statistics that will be used here is One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of single women who were hired for a secretarial job get married and quit work within two years after they are hired = $\frac{112}{200}$ = 0.56

n = sample of secretaries = 200

So, the test statistics = $\frac{0.56-0.80}{\sqrt{\frac{0.80(1-0.80)}{200} } }$

= -8.485

The value of z-test statistics is -8.485.

Now, at a 5% level of significance, the z table gives a critical value of -1.96 and 1.96 for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that different from 80% of all single women hired for a secretarial job get married and quit work within two years after they are hired.

We conclude that percent of all single women hired for a secretarial job get married and quit work within two years after they are hired is different from 80%.

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