1. A study reported in the Wall Street Journal found that of 899 home-based businesses, 369 were women-owned. This raises the question; do men or women own an equal number of home-based businesses? In terms of proportions, state the appropriate null and alternative hypotheses and explain in words what they mean. Define the acceptance and rejection region if a level of significance of 0.05 is selected. You first have to decide if you can use the normal distributions to approximate the sampling distribution of proportions. () Calculate the sample test statistic using the formula: #P - ZZ an d) Decide whether to accept or reject the null hypothesis. e) If the p-value were calculated to be 7.9064E-08, would you accept or reject the null hypothesis? 2. The Plunket Society (looks after babies and mothers at home in first 12 months) is interested in estimating the average number of maternity days women stay in the local maternity hospital. Assume Plunket believe that the outcome is better for women and their baby if they stay at least 5 days in hospital. A random sample is taken of 36 women who had babies in Auckland Hospital during the past year. The following table gives the key statistics for this sample Auckland Hospital Mean 3.25 Standard Error 0.197 Median 3 Mode Standard Deviation 1.180 Sample Variance 1.393 Kurtosis 0.199 Skewness 0.697 Range 5 Minimum Maximum 6 Sum 117 Count 36 i) Does the above table indicate that Plunket should be concerned that women are not staying long enough in hospital