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Problemsheet_5

# Problemsheet_5 - Hypothesis Testing Q1 The following are...

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Hypothesis Testing Q1 The following are sample results of measuring calorific contents (heat producing capacity in millions of calories per tonne) for samples drawn randomly from two adjacent coal mines: Mine 1: 1 x = 8, 230, 2 1 s = 15,750.25, 1 n = 5 Mine 2: 2 x = 7, 940, 2 2 s = 10, 920.25, 2 n = 6 Assuming that the calorific contents of the two coal mines are normally distributed with a common variance. Test the null hypothesis that the average calorific content of coal is the same for the two mines at 1% level of significance. Q2 A supermarket chain sells Dreyer’s Ice Cream for \$33.99 per quarter gallon. The management wishes to show that on average, rival supermarket chain sells Dreyer’s Ice Cream at higher prices. A random sample of 36 supermarkets of the rival company is taken and the price of a quarter Dreyer’s Ice Cream is recorded. The sample statistics are: x = \$34.99 and s = \$3.00. Formulate the suitable null and alternative hypotheses for the supermarket. What is the range of α that can be used and still guarantee that the test statistic will fall in the rejection region? Q3 An investment advisor wishes to determine whether Insurance Company A charges higher average premium than Insurance Company B for equivalent life insurance policies. She obtains the following on monthly premiums charged to 8 different people for life insurance coverage of \$US 250,000. (Note: premiums vary due to differences in age and health of the insured person.) Company A Monthly Premium \$364 \$375 \$350 \$359 \$372 \$355 \$367 \$359 Company B Monthly Premium \$358 \$372 \$355 \$351 \$372 \$347 \$356 \$360 (a) Is there sufficient evidence to suggest that Company A charges higher average monthly premiums than Company B? Use α = 0.025. (b) What is the lower bound on the significance level (i.e., p-value) of your test? Q4 An employment survey was conducted among one hundred UST graduates. The result

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is given in the following table. Number of job offers received 0 1 2 3 > 3 Number of students 5 40 15 30 10 (a) Let p denote the percentage of UST graduates who receive more than one job offer. Test the hypothesis that H 0 : p = 50% versus the alternative hypothesis H 1 : p > 50% at α = 5%. (b) In this survey, we also find that among those who received only one job offer the average monthly salary is \$10,300 with a standard deviation of \$1200, while the average monthly salary among those with three job offers is \$11,000 with a standard deviation of \$1500. Perform a test on the hypothesis that the mean salary for these two groups is the same and calculate the p-value. Q5 A government agency is investigating claims that male employees earn higher wages than female employees for similar jobs. Previous investigations suggest that salaries are normally distributed in most industries for both male and female employees. (a) A random sample of 11 male factory workers found a mean hourly wage of \$41.65 with a standard deviation of \$5.80. A random sample of 12 female factory workers found a mean salary of \$35.25 with a standard deviation of \$6.60. On the basis of these samples is it reasonable to conclude that male factory workers earn over \$1.50 more per hour on average than female factory workers? Use α = .05 and assume equal
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Problemsheet_5 - Hypothesis Testing Q1 The following are...

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