(b) assume 90 companies were included in the sample. what is the test statistic? (round your answer to three decimal places.)
Question
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A shareholders’ group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least nine years.a) The hypotheses that can be used to challenge the validity of the claim made by the shareholders’ group.H₀ : u ≤ 9Hₐ : u > 9So, the correct option is option (A).b) T- statistic value is -2.571 for a sample of 90 companies.c) The critical value for t i.e P-value is 0.0059d) P-value < α = 0.01, implies reject the null hypothesis. We can conclude that the mean tenure of a CEO is significantly lower than 9 years. The claim of the shareholders group is not valid. So, the correct option is option(D).We have given that,x-bar= 7.27 , σ = 6.38, n = 90a) Test that the mean tenure for a chief executive officer (CEO) was atleast nine years .Null and alternative hypothesis isH₀ : u <= 9Hₐ : u > 9b) test statistic:t =( x-bar – μ ) /σ/√n=> t = (7.27 – 9 )/6.38/90=> t = – 1.73/0.67251=> t = -2.571c) P-value :P-value = P( tₙ₋₁ < t) = P(t₉₀₋₁ < t )=> P-value = P( t₈₉< – 2.571)=>P-value = P( t₈₉ >2.571)=> P-value = 1 – P( t₈₉< 2.571)P-value = 1 – 0.9941 = 0.0059d) Significance level, = 0.01we see that p-value= 0.0059 < 0.01Decision : Reject the null hypothesis H₀We have no evidence to support the claim.Hence, we calculate all the required result.To learn more about Null Hypothesis , refer:https://brainly.com/question/15980493#SPJ4Complete 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 = 7.27 yearsfor CEOs with a standard deviation ofs = 6.38 years.(a)Formulate hypotheses that can be used to challenge the validity of the claim made by the shareholders’ group. multiple choice:i)H0: μ ≤ 9Ha: μ > 9ii)H0: μ ≥ 9Ha: μ < 9iii) H0: μ > 9Ha: μ ≤ 9iv)H0: μ < 9Ha: μ ≥ 9v) H0: μ = 9Ha: μ ≠ 9(b)Assume 90 companies were included in the sample. What is the test statistic? (Round your answer to three decimal places.)c)What is the p-value for your hypothesis test? (Round your answer to four decimal places.)p-value =(d) At = 0.01,what is your conclusion? MULTIPLE CHOICE:
- Do not reject H0. We cannot conclude that the mean tenure of a CEO is significantly lower than 9 years. The claim of the shareholders group is valid.
- Reject H0. We can conclude that the mean tenure of a CEO is significantly lower than 9 years. The claim of the shareholders group is not valid.