Question

1) Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95​% confidence that the sample mean is ±7 IQ points of the true mean. Assume that the standard deviation is

19 and determine the required sample size.

2) There are many reasons adults use credit cards. A recent survey found that 47​%

of adults used credit cards for convenience.

a. To conduct a​ follow-up study that would provide 95​% confidence that the point estimate is correct to within

±0.02 of the population​ proportion, how many people need to be​ sampled?

b. To conduct a​ follow-up study that would provide 95​% confidence that the point estimate is correct to within

±0.06 of the population​ proportion, how many people need to be​ sampled?

c. Compare the results of​ (a) and​ (b).

3)A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 100 greeting cards indicates a mean value of $ 2.93 and a standard deviation of $ 0.58

a. Assuming a normal​ distribution, construct a 90 % confidence interval estimate of the mean value of all greeting cards in the​ store's inventory.

b. Suppose there were 2,000 greeting cards in the​ store's inventory. How are the results in part​ (a) useful in assisting the store owner to estimate the total value of her​ inventory?

If possible, please explain how to do in excel or ph stat. Thank you in advance for your help!!

Answer 1

1)

Solution :

Given that,

Population standard deviation = = 19

Margin of error = E = 7

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

sample size = n = (Z_/2* / E) ²

n = (1.96 * 19 / 7)²

n = 28.3

n = 29

Sample size = 29