Question

You wish to test the following claim (Ha) at a significance level of a 0.02 Ho: μ 52.4 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data ColumnA Column B Column C Column D Column E 62.1 44.7 56.5 61.3 55.8 65.1 35.1 71.4 60.5 43.8 55.1 58.7 70.7 52 66.1 69.4 80.4 70 72.9 59 55.8 30.3 80.4 48.8 63.8 60.1 62.1 62.1 73.8 46 69.4 42.8 61.7 63.8 51 58.3 37.5 58.3 63.3 50.6 58.3 35.1 59 52.7 48.8 54.1 48.8 69.4 45.6 80.4 55.1 60.1 30.3 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to)a greater than a This test statistic leads to a decision to reject the null accept the null fail to reject the null1 As such, the final conclusion is that... OThere is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 52.4 There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 52.4 The sample data support the claim that the population mean is not equal to 52.4 There is not sufficient sample evidence to support the claim that the population mean is not equal to 52.4

Answer 1

null hypothesis Alternate Hypothesis 52.4 52.4 for 0.02 level with two tailed test and n-1-54 degree of freedom, critical value of t- Decision rule 2.397 reject Ho if absolute value of test statistic t2.397 population mean sample mean sample size sample std deviation 52.4 57.21 55.00 12.30 nE s= standard errror of means sx-s/in= 1.659 test statistic p value t 2.897 0.0054

test statistics =2.897

p value =0.0054

the p value is less than alpha

reject the null

the sample data support the claim