Question

A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least nine years. A survey of companies reported in the Wall Street Journal found a sample mean tenure of x = 7.74 years for CEOs with a standard deviation of s = 6.45 years. a. Formulate hypotheses that can be used to challenge the validity of the claim made by the shareholders' group Select your answer+ Ha : -Select your answer- 9 b. Assume 60 companies were included in the sample. What is the p-value for your hypothesis test? Enter negative value as negative number. t-value (to 3 decimals) p-valueSelect your answer c. At a-0.01, what is your conclusion? hypothesis We enough evidence to disprove the shareholder group's claim # the nu Select your answer Select your answer- Joe believes the average battery life of a vehicle is equal to 9 years. A sample of 5 vehicles was taken and the following data on battery lives was obtained. Assume the distribution of the population is normally distributed. Vehicle 4 7.6 Years 6. 8. 9 What is the value of the test statistic? a. 7.26 b. .010 c. Not enough information is given to compute the test statistic. .-4.54

Answer 1

Solution:-

1)

a) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u > 9
Alternative hypothesis: u < 9

Note that these hypotheses constitute a one-tailed test. .

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.8327
DF = n - 1

D.F = 59
b)

t = (x - u) / SE

t = - 1.51

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of - 1.51

Thus the P-value in this analysis is 0.068.

Interpret results. Since the P-value (0.068) is greater than the significance level (0.01), we failed to reject the null hypothesis.

c) Failed to reject the null hypothesis, We do not have enough evidence to disprove the shareholder group's claim.