Explanation Calculation: The data represents the record high and low for the span years of 1871-2013. In this context, eliminate the year that repeats more than once. In the data set, * represents the records that occurred more than once. After eliminating the repeated years, the sample size of the year is 40. Assumptions for performing a hypothesis test about μ when σ is unknown: The samples taken from the population are simple random samples. The sample size should be large that is, n > 30 or the population should be distributed according to normal. Requirement check: The sample of 40 years was assumed to be selected at random. It is assumed that the population is distributed to normal. Thus, the condition is satisfied. Step 1: Denote μ as true mean years. The test hypotheses are given below: Null hypothesis: H 0 : μ = 1942 That is, the mean year in which a record low occurred is 1942. Alternative hypothesis: H 1 : μ < 1942 That is, the mean year in which a record low occurred is less than1942. Step 2: Assume that the level of significance is 0.05. Step 3: Test statistic: The t- test statistic is: t = x ¯ − μ s n , Where, x ¯ be the sample mean, μ be the hypothesized mean and s be the sample standard deviation and n be the sample size

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ISBN: 9781259570643

Author: Navidi

Publisher: MCG

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Chapter 8, Problem 6CS

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Check whether it can be concluded that the mean year in which a record low occurred is less than1942.

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