Explanation Given info: To examine the average cost of the movie ticket, a random sample of 15 movie tickets cost is noted. The results based on the survey is x ¯ = $ 11.09 and s = $ 4.86 . The additional information is about the population parameter is μ = $ 7.89 and level of significance α = 0.01 . Calculation: The testing hypotheses are given below: Null hypothesis H 0 : H 0 : μ = 7.89 Alternative hypothesis H 1 : H 1 : μ > 7.89 Here, the information about the population standard deviation is not revealed. Thus, z -test about mean cannot be applied in this case. Requirements for t-test about mean when population standard deviation ( σ ) unknown: The sample must be drawn randomly from the desired population. The sample must be greater than or equal to 30, if not the population must be approximately normal. Here, the sample size is less than 30 and but the sample is drawn randomly. Hence, an assumption about the normality of the population has to be made. Thus, t- test about mean can be valid in this case. Decision rule based on classical approach: If t > t α , then reject the null hypothesis H 0 . Critical value: For the level of significance α = 0.01 . Degrees of freedom: The sample size is n = 15 . The degrees of freedom is obtained as, d . f = n − 1 = 15 − 1 = 14 From Table F of the t- distribution from Appendix A under one tail, the critical value is 2

Elementary Statistics: A Step By Step Approach

9th Edition

ISBN: 9780073534985

Author: Allan Bluman

Publisher: McGraw-Hill Science/Engineering/Math

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Chapter 8.3, Problem 17E

To determine

To test: Whether there is any sufficient evidence to infer that the average cost of movie ticket is greater than $7.89.

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Chapter 8.3, Problem 16E

Chapter 8.3, Problem 18E

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Chapter 8 Solutions

Elementary Statistics: A Step By Step Approach

Ch. 8.1 - Applying the Concepts 81 Eggs and Your Health The...Ch. 8.1 - Define null and alternative hypotheses, and give...Ch. 8.1 - What is meant by a type I error? A type II error?...Ch. 8.1 - What is meant by a statistical test?Ch. 8.1 - Explain the difference between a one-tailed and a...Ch. 8.1 - What is meant by the critical region? The...Ch. 8.1 - What symbols are used to represent the null...Ch. 8.1 - What symbols are used to represent the...Ch. 8.1 - Explain what is meant by a significant difference.Ch. 8.1 - When should a one-tailed test be used? A...

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