PLEASE SHOW WORK The National Quality Research Center provides a quarterly measu

Question

PLEASE SHOW WORK

The National Quality Research Center provides a quarterly measure of consumer opinion about product services. A survey of 10 restaurants in the Fast Food/Pizza group showed a sample mean customer satisfaction index of 71. Past data indicate that the population standard deviation of the index has been stable with a value of 5. (a) Compute a 95% interval estimate of customer satisfaction index of restaurants in the Fast Food/Pizza group. Show your steps and manual (hand and calculator) calculations in 4 decimal places, where possible. (b) Interpret your estimate in (a) above. (c) What assumption is required for your estimate above to be valid?

Explanation / Answer

we knwo that the confidence interval is given as

Mean +- z*sd/sqrt(n) , here mean = 71 , sd = 5 and n = 10 , also for 95% CI the value of z score from the table is 1.96

putting the values in the equation and solving for plus and minus sign we get

71+- 1.96*5/sqrt(10)

67.9 and 74

This means that we are 95% confident that the true value of the mean of customer satisfaction index would lie in the interval 67.9,74

The data must follow normal distribution for the assumption to be valid

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