Statistics help

A) Calculate the point estimate for the population proportion of successes. (Do not round intermediate calculations. Round your answer to 3 decimal places.)

B) Construct an 90% and a 95% confidence intervals for the population proportion. (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answers to 3 decimal places.)

C) Can we conclude at 90% confidence that the population proportion differs from 0.400?

Please select one of the following.

C1) Yes, since the confidence interval contains the value 0.400.

C2) Yes, since the confidence interval does not contain the value 0.400.

C3) No, since the confidence interval contains the value 0.400.

C4) No, since the confidence interval does not contain the value 0.400.

D) Can we conclude at 95% confidence that the population proportion differs from 0.400?

Please select one of the following.

D1) No, since the confidence interval contains the value 0.400.

D2) No, since the confidence interval does not contain the value 0.400.

D3) Yes, since the confidence interval contains the value 0.400.

D4) Yes, since the confidence interval does not contain the value 0.400.

2. A machine that is programmed to package 1.34 pounds of cereal is being tested for its accuracy. In a sample of 49 cereal boxes, the sample mean filling weight is calculated as 1.34 pounds. It can be assumed that filling weights are normally distributed with a population standard deviation of 0.07 pound. Use Table 1.

A) Identify the relevant parameter of interest for these quantitative data.

Please select one of the following

A1) The parameter of interest is the proportion filling weight of all cereal packages.

A2) The parameter of interest is the average filling weight of all cereal packages.

B) Compute the point estimate as well as the margin of error with 90% confidence. (Round intermediate calculations to 4 decimal places. Round "z" value and final answers to 2 decimal places.)

C) Calculate the 90% confidence interval. (Use rounded margin of error. Round your answers to 2 decimal places.)

D) Can we conclude that the packaging machine is operating improperly?

Please select one of the following

D1) Yes, since the confidence interval contains the target filling weight of 1.34.

D2) Yes, since the confidence interval does not contain the target filling weight of 1.34.

D3) No, since the confidence interval contains the target filling weight of 1.34.

D4) No, since the confidence interval does not contain the target filling weight of 1.34.

E) How large a sample must we take if we want the margin of error to be at most 0.01 pound with 90% confidence? (Round intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places and round up your final answer to the next whole number.)

3. At a new exhibit in the Museum of Science, people are asked to choose between 65 or 159 random draws from a machine. The machine is known to have 70 green balls and 59 red balls. After each draw, the color of the ball is noted and the ball is put back for the next draw. You win a prize if more than 64% of the draws result in a green ball. Use Table 1.

A) Calculate the probability of getting more than 64% green balls.(Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

B) Would you choose 65 or 159 draws for the game?

4. Last year, the typical college student graduated with $25,900 in debt (The Boston Globe, May 27, 2012). Let debt among recent college graduates be normally distributed with a standard deviation of $6,000. Use Table 1.

A) What is the probability that the average debt of two recent college graduates is more than $21,000? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

B) What is the probability that the average debt of two recent college graduates is more than $26,000? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

5. A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 68, 73, 41, 25, 43, 23, and 58. It can be assumed that weekday customer visits follow a normal distribution. Use Table 2.

A) Construct a 90% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places and "t" value to 3 decimal places, and final answers to 2 decimal places.)

B) Construct a 99% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places and "t" value to 3 decimal places, and final answers to 2 decimal places.)

C) What happens to the width of the interval as the confidence level increases?

Please select one of the following

C1) As the confidence level increases, the interval becomes wider and less precise.

C2) As the confidence level increases, the interval becomes narrower and less precise.

6) Acceptance sampling is an important quality control technique, where a batch of data is tested to determine if the proportion of units having a particular attribute exceeds a given percentage. Suppose that 11% of produced items are known to be nonconforming. Every week a batch of items is evaluated and the production machines are adjusted if the proportion of nonconforming items exceeds 15%. Use Table 1.

A) What is the probability that the production machines will be adjusted if the batch consists of 52 items? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

B) What is the probability that the production machines will be adjusted if the batch consists of 104 items? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

7) The monthly closing stock prices (rounded to the nearest dollar) for Panera Bread Co. for the first six months of 2010 are reported in the following table. Use Table 2.

A) Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4 decimal places and "sample mean" and "sample standard deviation" to 2 decimal places.)

B) Compute the 95% confidence interval for the mean stock price of Panera Bread Co., assuming that the stock price is normally distributed. (Round "t" value to 3 decimal places, and final answers to 2 decimal places.)

C) What happens to the margin of error if a higher confidence level is used for the interval estimate? Please select one of the following

C1) The margin of error increases as the confidence level increases.

C2) The margin of error decreases as the confidence level increases.

8) A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The management decides to evaluate the satisfaction surveys of its next 50 customers. The dealer will be fined if the number of customers who report favorably is between 25 and 27. The dealership will be dissolved if fewer than 25 report favorably. It is known that 67% of the dealer’s customers report favorably on satisfaction surveys. Use Table 1.

A) What is the probability that the dealer will be fined? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

B) What is the probability that the dealership will be dissolved? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)