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# Hypothesis testing for a grocery store and national safety council

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Each part (a-d) of this problem gives the population standard deviation σ;, the statement of a claim about μ, the sample size n, the desired level of significance α. Formulate
(i) the hypotheses,
(ii) the test statistic Z,
(iii) the rejection region.
the answers to part (a) are provided.

(a) σ = 2 claim: μ > 30, n = 55, α = .05
(b) σ = .085 claim: μ < .15 n = 125 α = .025
(c) σ = 8.6 claim μ≠ 80 n = 38 α = .01
(d) σ = 1.23 claim μ ≠ 0 n = 40 α = .06

6.A sample of 40 sales receipts from a grocery store has x = \$141 and s= \$30.2. Use these values to perform a test of Ho:μ = 150 against Ha:μ <150 with α = .05.

7.Calculating from a random sample of 36 observations, one obtains the results x = 80.4 and s=16.2. In the context of each of the following hypothesis testing problems, determine the P-value o these results and state whether or not it signifies a strong rejection of Ho:

(a) To test Ho:μ = 74 versus μ > 74
(b) To test Ho:μ = 85 versus Ha:μ < 85
(c) To test Ho:μ =76 versus Ha:μ≠ 76

8.A national safety council wishes to estimate the proportion of automobile accidents that involve pedestrians. How large a sample of accident records must be examined to be 98% certain that the estimate does not differ from the true proportion by more than .03? (The council believes that the true proportion is below .25)

https://brainmass.com/statistics/hypothesis-testing/hypothesis-testing-grocery-store-national-safety-council-78108

#### Solution Preview

5. NOTE: o represents null

Each part (a-d) of this problem gives the population standard deviation σ, the statement of a claim about μ, the sample size n, the desired level of significance α. Formulate
(i) the hypotheses,
(ii) the test statistic Z,
(iii) the rejection region.
the answers to part (a) are provided.

(a) σ = 2 claim: μ > 30, n = 55, α = .05
(i) H0: μ = 30, H1: μ > 30
(ii) Z=
(iii) R: Z ≥ 1.645

(b) σ = .085 claim: μ < .15 n = 125 α = .025
(i) H0: μ = .15, H1: μ < .15
(ii) Z=
(iii) R: Z -1.96

(c) σ = 8.6 claim μ ≠ 80 n = 38 ...

#### Solution Summary

The solution explains how to formulate hypothesis tests, calculate p-values, and test statistics in four questions referring to a grocery store chain and a national safety council.

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