Statistics and Probability Answers

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) Let p2 be the true proportion of all TV-viewing families who watched the premiere of “Music Music on TV3”. Estimate p1 − p2 and obtain a 95% confidence interval for p1 − p2.

(b) From the results in part (a), can you 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.

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 p1 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?

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?

In a sample of 50 turnings from an automatic 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.

The manager of AllNeeds supermarket wants to estimate µ,, 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 µ.

(b) Based on 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?

Dan tossed unbiased coin , on each toss he wins 50 pesos if head appears and losses 40 pesos if tail appears. What will be the expected value and variance of his gain?​

If a delivery of dairy products weight 320 Kg, how many kilograms is expected to last beyond 10 days

Given a set of number S = (2,4,7,10,13,16,22,27,81,102). If a number is picked at random, find the probability that the number is even or prime.

The average weight of 50 senior high school students is 52 kg with a standard deviation of 2.5

kg. If 25 students are randomly selected, find the mean, standard deviation, and variance of the

corresponding sampling distribution of the sample means

The average cost per household of owning a brand new car is Php 5,000. Suppose that we randomly selected 40 households, determine the probability that the sample mean for these 40 households is more than Php 5,350. Assume that the variable is normally distributed and the standard deviation is Php 1,230.

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