Problem 1) A supermarket manager is trying to decide how many check out register

Question

Problem 1)

A supermarket manager is trying to decide how many check out registers to keep open during early morning hours. To aid her analysis she recorded the number of customers who came to the supermarket during early morning hours for the past 12 days. The data collected for the 12 days are:

167, 172, 150, 178, 160, 164, 167, 140, 190, 150, 162, 157.

a) Construct a 95% confidence interval for the mean number of early-morning customers in the supermarket.

b) What assumption must you make in order to construct your confidence interval? Do the data indicate the violation of this assumption?

Problem 2)

Your friend wants to play a game with you involving a die, which she claims is fair. Assume that her claim is correct.

a) Consider a sample proportion of even faces in 100 flips. What is the mean, standard deviation and distribution of this sample proportion?

b) How would your answers to a) changed if the sample proportion were based on 25 flips of a fair die? Explain

c) What is the probability that the sample proportion of even faces in 100 flips of a die will be between 0.45 and 0.55? Suppose that in 100 flips of die, 38 resulted in an even face.

d) Construct a 98% confidence interval for the probability of a die coming up even face and interpret it .Based on your confidence interval is your friend’s claim correct? If it isn’t how is the die biased?

e) What is the margin of error of the confidence interval in a)?

f) What sample size would you need to obtain a 98% confidence interval for the probability of a die coming up even face with the margin of error of not more that 0.05? 1

Problem 3)

A commercial for a household appliances manufacturer claims that about 6% of all products sold require a service call in the first year. A consumer protection agency wants to check this claim by surveying 400 households that purchased one of the company’s appliances.

a) What is the probability that in a sample of 400 households more than 10% require the service call within the first year?

b) In the sample of 400 households it was found that 44 required a service call within the first year. What is your reaction to the commercial’s claim?

Problem 4

National Institute of Health (NIH) using a random sample of 400 from the population of US teenagers obtained the following confidence interval for the proportion of US teenagers who smoke cigarettes (01671 02329)

a) What is the number of teenagers in the sample of 400 who smoke cigarettes?

b) What is the margin of error and the confidence level of this interval? c) What is the largest possible margin of error of a 98% confidence interval for the population proportion based on a random sample of size = 400?

Explanation / Answer

a)

The 95% confidence interval is 154.55 to 171.61

b) We assume the data is normally distributed

Null hypothesis: "The data can be modelled according to the normal distribution."
When the P value is small enough you can conclude that the data set is not following the normal distribution

Here P value is P > 0.20 Hence its a normal data

PS: We are directed to solve only first if multiple questions are posted

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