A famous welfare association in Karachi claims that it takes 9 minutes on average to reach its destination in emergency situations. To test this claim, the agency which licences ambulance services had them timed on 50 emergency calls, getting a mean of 10.4 minutes with a standard deviation of 2 minutes. At the 5% significance level test the claim that the average time the ambulance takes to reach its destination is 9 minutes.
a) A famous welfare association in Karachi claims that it takes 9 minutes on average to reach its destination in emergency situations. To test this claim, the agency which licences ambulance services had them timed on 50 emergency calls, getting a mean of 10.4 minutes with a standard deviation of 2 minutes. At the 5% significance level test the claim that the average time the ambulance takes to reach its destination is 9 minutes.
b) It is believed in a renowned courier service that packages delivered at the beginning of the month are lighter than those delivered at the end of the month. As an experiment a random sample of 15 packages are weighed at the beginning of the month and it is found that mean weight was 6.25 kgs with a standard deviation of 1.18 kgs. A random sample of 12 packages have also been weighed at end of the month and it is found that mean weight was 4.86 kgs with a standard deviation of 1.14 kgs. At the 99% level of significance, test the claim that packages at the beginning of the month are lighter.
c) A developer is considering two alternative sites for a regional shopping center. Since household income in the community is one important consideration in such site selection, the developer wishes to test the null hypothesis that there is no difference between the mean household income amounts in the two communities. Consistent with this hypothesis, it is assumed that the standard deviation of household income is also the same in the two communities. For a sample of 29 households in the first community, the average annual income is $44,500 with the sample standard deviation $1,700. For a sample of 40 households in the second community, average annual income is $43,200 and standard deviation is $2,250. Test the null hypothesis at the 5 percent level of significance.
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