1. The manager of All Needs supermarket wants to estimate p,, the average amount of money spent per week for groceries by each student, assuming this amount of money follows approximately a normal distribution. A random sample of 90 is taken, of which the mean and standard deviation of the amount of money spent per week for groceries are GHC81.50 and GHC10.36 respectively. 

(a) Calculate a 99% confidence interval for H. 

(b) Based an your result in (i), would you say on average a student spends more than GHC30?

(c) How many students must be surveyed if the manager wanted to estimate the true average spending of students within a margin of .10 with probability 95? 

2. Independent random samples from normal distributions with equal variance of the amount of insider trading during mergers by employees of investment banking firms (1) and brokerage houses (2) gave the results listed in the accompanying table.

 

(a) Find the 95% confidence interval estimate for the difference between means - l2.. 

(b) Would you conclude that employees of Investment banking firms cause more insider trading than their counterparts in Brokerage House? 

3. In a sample of 50 turnings from an automatics lathe 8 were found to be outside specifications. The cutting bits were then changed and the machine restarted. A new sample of 50 contained 3 defective turnings. Find a 90% confidence interval for the decrease in the proportion defective after changing bits. 

4. If a normal population of overpayments by National Health Insurance Authority to a private health service provider is known to have a population standard deviation equal to GHC5. how large a sample would we take in order to be 95% confident that the sample mean overpayment will not differ from the population mean overpayment by more than +0.80? 

5. Television advertisers value the well-known Radio and TV awards scheme RTP as a measure of a TV/Radio show's popularity among viewers. The RTP rating of a certain TV program is an estimate of the proportion of viewers, expressed as a percentage, who watch the program on a given day. In one survey, the RTP ratings team found that 101 out of 165 sampled families watched "The KSM Show" on the night of its premiere (the first time it is shown on television). In a separate survey several years later, the RTP ratings team found that 97 out of 180 sampled families watched "Music Music on TV3" on its premiere. 

(a) Estimate the true proportion pi of all TV-viewing families who watched the premiere of "The KSM Show" and obtain a 95% confidence interval for p1. 

(b) Briefly explain what this 95% confidence interval means. 

(c) If the RTP team wanted to guarantee that all proportions are estimated to within +0.05 with 95% confidence, how large should their samples be? 

(d) Let p2 be the true proportion of all TV-viewing families who watched the premiere of "Music Music on TV3". Estimate pi – P2 and obtain a 95% confidence interval for pi - p2. 

(e) From the results in part (d), can ycu tell whether the premiere of "The KSM Show" was more popular that the premiere of "Music Music on TV3"? Give a brief justification of your answer. TAT 223, March 2022 Pago 1 of 1 RM/CC-W

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