Question

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

Answer 1

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.