Question

You wish to test the following claim (Ha) at a significance level of a 0.01 You obtain the following two samples of data. Sample #1 Sample #2 81.473.489.6 102.2 76 55.3 102.277.5 110.8 77.9 94.576.5 108.5 105 88.4113.9 91.6 90.8 59.9 79.3 90 90.861.6 93.7101.6 78.4103.5 100.4 65.397.8 84.6 95.459.9 102.9 70.3 92 71.6 68.8105.895.4 68 100.4 101 68 96.3 109.6 85.7 73.5 96.4 85.384.1 74.481.5 88.474.8 96.4 102.3 81.2 74.486.475.6 76.4 85.3 95.9 68 63.486.1 102.375.6 82.7 73.5 84.4 89.175.6 78.8 79.3 93.7 68 73 84.17 108.5 82.6 92 89.495.5 92 93.4 83.484.6 98.3 89.688.1 71.6 93.751.1 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? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.) p-value- The p-value is... Oless than (or equal to) a O greater than α This test statistic leads to a decision to.. Oreject the null O accept the null Ofail to reject the null As such, the final conclusion is that. There is sufficient evidence to warrant rejection of the claim that the first population mean is greater than the OThere is not sufficient evidence to warrant rejection of the claim that the first population mean is greater than OThe sample data support the claim that the first population mean is greater than the second population mean. second population mean the second population mean. O There is not sufficient sample evidence to support the claim that the first population mean is greater than the second population mean.

Answer 1

Null hypothesis. H。 $14 Alternative hypothesis, H1 :4 > μ2 Level of significance, α = 0.05. The test is one tail (iight tail Calculate the test statistic: By using the excel (Mega stat) software to determine the test statistic and p-value with the help following procedure 1. Enter the data in excel sheet. 2. Click on add ins in the excel tool bar 3. Choose hypothesis tests→ compare two independent groups. 4. In hypothesis compare two independent groups dialog box, choose data input and enter the input range of sample 1 and sample 2. 5. Enter hypothesis difference is 0-alternative hypothesis not equal-> t test(un equal variance)→ 99% confidence interval. 6. Click ok. To get the required output is given below:

Hypothesis Test: Independent Groups (t-test, unequal variance) Group 1 Group 2 86.767 83.766 mean 15.3079.637 std. dev. 35 n 60 92 df 3.0010 difference (Group 1 - Group 2) 2.5609 standard error of difference 0 hypothesized difference 1.172t 1221 p-value (one-tailed, upper) 3.7350 confidence interval 99.% lower 9.7369 confidence interval 99.% upper 6.7360 margin of error From the above output, the test statistic is 1.172 The p-value of the hypothesis test is 0.1221

Compare the p value with a. Reject Ho, if p α otherwise do not reject H, e is greater than the si Since the p-valu gnificance level The test statistic leads to decision to fail to reject the null hypothesis at 1% level of Decision: There is not sufficient sample evidence to support the claim the first population mean is greater than the second population mean.