This is Marketing Research. I need to show my work. Formulii Sample Size (Mean)

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This is Marketing Research. I need to show my work.

Formulii Sample Size (Mean) n s Proportion ? 22[P(1.pl Standard Error (Mean)s--? Proportion sp P(1-P) (5 is for population deviation) (Sr is the sample estimate) , is the population proportion error) (sp is the sample estimate) ( Interval (Mean) X t zsr Proportion pt zsp Sp X is the sample mean) (u is the hypothesized mean) (P is the sample percentage) (u is the hypothesized percentage) 1. Calculate the following: (Must show your formula used and appropriate numbers for each formula variable.) A. (2 Pts) Given: Mean (150), Standard Deviation (30) Confidence level (95%), Sample (200) Calculate the Confidence Interval B. (2 pts)Given: Percent (76), Confidence Level (99%), Sample (300) Calculate the Confidence Interval C. (6 Pts) At 95 percent confidence leve company's program. You decide to test this company's hypothesis by taking a sample of the firm's college interns. You find that your sample of 100 agents has a sample mean of $2,800 and a standard deviation of $350. Ihe question is whether this sample mean deviates f the hypothesized sufficiently to reject the firm's claim, that is, does the deviation's value fall within/without two standard deviations of the hypothesized mean? Hence, do you accept the firm's Mean hypothesis or reject it? 1, an intern can earn $2,750 per semester working in a

Explanation / Answer

A.

CI for 95%

n = 200

mean = 150

z-value of 95% CI = 1.9600

std. dev. = 30

SE = std.dev./sqrt(n) = 2.12132

ME = z*SE = 4.15771

Lower Limit = Mean - ME = 145.84229

Upper Limit = Mean + ME = 154.15771

95% CI (145.8423 , 154.1577 )

B.

n = 300

p = 0.76

z-value of 99% CI = 2.5758

SE = sqrt(p*(1-p)/n) = 0.02466

ME = z*SE = 0.06351

Lower Limit = p - ME = 0.69649

Upper Limit = p + ME = 0.82351

90% CI (0.6965 , 0.8235 )

C.

n = 100, xbar = 2800, sd = 350

SE = 350/sqrt(100) = 35

xbar - 2*SE = 2800 - 70 = 2730

xbar + 2*SE = 2800 + 70 = 2870

As value 2750 lies in the above CI of (2730, 2870), we fail to reject the null hypothesis.

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