MATH 2565 - Winter 2019 Assignment 4 Question 1: Sample size, n
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MATH 2565 - Winter 2019 Assignment 4 Question 1: Sample size, n = 560 ; sample proportion,; a.The null and alternative hypothesis are defined as: The critical value atis:(left-tailed test) The test statistic is calculated as: The test statistic is less than the critical value (-2.732≤-2.326), we reject the null hypothesis. Therefore, there is sufficient statistical evidence to suggest that the true proportion of residents who favor additional power to tap phones is less than 0.75. b.The p-value associated with this hypothesis test is: p = 0.0031; hence p-value < 0.01 Question 2: Sample size, n = 15; sample mean,= 3.63; sample standard deviation, s = 1.67; α = 0.05 The null and alternative hypothesis are defined as: Since the sample size is small (n<30), the appropriate test statistic is: This is a right tailed test, using a t test statistics and 5% significance level. The critical value atand degrees of freedom, df= 15-1=14 is: The decision rule is to Rejectif t≥2.145
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The test statistic is calculated as: The test statistic, T= 1.461 is less than the critical value, t =2.145, we fail to reject the null hypothesis. Therefore, there is no statistically sufficient evidence atto suggest that the true population mean FEF is greater than 3.0. Question 3: Historical mean thickness = 3.32 meters; sample size, n = 28; sample mean,= 4.036 meters; σ = 2.8 meters; assuming it’s normally distributed. a.The null and alternative hypothesis are defined as: Since the sample is normally distributed, the appropriate test statistic is:. This is a two tailed test, using a z test statistics and 1% significance level. The critical value of t is:. The decision rule is to Rejectif z≤-2.576 or z≥ 2.576. The test statistic is computed as: The conclusion is not to reject the null hypothesis because 1.353≤2.771. Therefore, there is no statistically significant evidence at α=0.01 to show that there is any change in the mean ice thickness. b. 2743.07257.016049.01ZP