Question

You wish to test the following claim (Ha) at a significance level of α=0.01.       Ho:μ1=μ2
      Ha:μ1≠μ2 You obtain the following two samples of data.

Test statistic

P value

Accept or reject the null

Sample #1		101.8 54.7 76.6 106.8 91.5 83.8 84.1 96.4 80.7 83.2 94.4 89.6 71.2 81.9 87.3 89.6 93.1 60.2 91.1 103.9 85.4 82.3 90 74.3 98.7 100.9 96.4 74.7 95.8 98.1 67.6 81.3 72.6 96.9 68.9 92.3 90.4 70.1 102.8 82.6 79.7 73.9 78.7 83.8 100.1 63.1 61.8 103.9 83.5 85.1 72.6 88.3 86.6 93.1 82.9 63.1 80.7 65.2 77.4 98.7 77.7 64.2 76.6

Sample 2

87.8	63.9	69.3	70.5
68	54.7	117.8	129.8
66.7	90.6	57	59.8
64.6	115.6	103	68.7
82.4	57	91.7	67.4
71.1	100.4	58.9	65.3
91.1	89.4	67.4	76.1
110.6	42.3	60.7	66.7
54.7	79.8	75	74.5
103.9	109.3	87.2	106.9
66.7	77.7	61.6	110.6
62.4

Answer 1

Answer Date: 11/11/2019 To test the hypothesis is that there is a difference between two population means at 1% significance level. The null and alternative hypothesis is, Holly = 112 H : U12 The t-test statistics is, By using Excel software, find t-test statistics with the help of following steps: 1) Import the data. 2) Select t-test: Two Sample Assuming Une qual Variances from Data Analysis in Data menu. Select Variable 1 Range and Variable 2 Range. Give Hypothesized Mean Difference. Select Labels and give Alpha. Choose Output Range from Output options. Click Ok.

t-Test: Two-Sample Assuming Unequal Variances Sample 1 Sample 2 83.884127 79.03556 155.03007 420.6919 63 45 0 Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 67 1.4109057 0.0814495 2.3833025 0.1628989 2.6512197 From the Excel output, the t-test statistics is 1.411. The p-value for this test is, From the Excel output, the p-value for this test is 0.1629

Decision The conclusion is that p-value in this context is greater than 0.01 which is 0.1629, so the null hypothesis is not rejected at 1% level of significance. There is insufficient evidence to indicate that there is a difference between two population means. The result is not statistically significant.