Question

You wish to test the following claim (H1) at a significance level of α=0.001.

      Ho:μ1=μ2
      H1:μ1>μ2

You obtain the following two samples of data.

Sample #1	Sample #2
97.5 85.7 94.6 100.3 81.4 95.2 83.1 94.9 87.5 96.6 92.7 82.1 85.2 77.8 91.5 101.7 85.7 90.8 88.4 86.5 98.1 81.4 88.7 95.2 86.5 83.4 92.9 102.8 95.7 94.1 95.4 88.9 89.1 102.8 83.4 99.5 90.8 106.6 93.6 81.4 96.6 93.9 88.2 86.2 96 96 102.2 75.8 86.5 99.9 84.6 98.5	89.5 85.2 71.6 82.5 87.6 76 93.8 111.8 75.2 91.5 93.8 73.9 96.5 73.5 68.5 93.8 87 80.7 86.4 66.9 81.3 102.6 80.7 73 81.6 69.2 81 87.6 56.8 98.2 71.6 84.6 73.9 87.9 76 88.8 96.5 97.6 93 63.6 92.3 67.7 74.8 85.5 73 76.3 108.5 87.6 77.8 103.7 71.6 91.2 84.6

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) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail 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 second population mean.
• There is not sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean.
• The sample data support the claim that the first population mean is greater than the second population mean.
• There is not sufficient sample evidence to support the claim that the first population mean is greater than the second population mean.

Answer 1

The given data is,

Sample #1		Sample #2
97.5	85.7	94.6	100.3		89.5	85.2	71.6	82.5
81.4	95.2	83.1	94.9		87.6	76	93.8	111.8
87.5	96.6	92.7	82.1		75.2	91.5	93.8	73.9
85.2	77.8	91.5	101.7		96.5	73.5	68.5	93.8
85.7	90.8	88.4	86.5		87	80.7	86.4	66.9
98.1	81.4	88.7	95.2		81.3	102.6	80.7	73
86.5	83.4	92.9	102.8		81.6	69.2	81	87.6
95.7	94.1	95.4	88.9		56.8	98.2	71.6	84.6
89.1	102.8	83.4	99.5		73.9	87.9	76	88.8
90.8	106.6	93.6	81.4		96.5	97.6	93	63.6
96.6	93.9	88.2	86.2		92.3	67.7	74.8	85.5
96	96	102.2	75.8		73	76.3	108.5	87.6
86.5	99.9	84.6	98.5		77.8	103.7	71.6	91.2
		84.6

Here we wish to test the following claim (H1) at a significance level of α=0.001.

      Ho:μ1=μ2 V/s
      H1:μ1>μ2

The test statistic for this sample is,

Z=4.203

What is the p-value for this sample?
p-value =0.0000132

The p-value is.

• less than α=0.001

This test statistic leads to a decision to,

• reject the null

As such, the final conclusion is that.

• The sample data support the claim that the first population mean is greater than the second population mean.

Explanation:

from the given dato, Iwe have n = 52 h2=53 x = 91.42 X2 = 83.50 Sample, vanance (5,2) - 50.63 Sample 2 variance (53) = 136.36. Where s2 = {(x,; -7,2 D 522 Z (Xai - X 2) 2 1-1 We wish to test population mean of ist Sample is greater than population sample. That is, to test, mean of and Hor 4, = ela tapeet r/s H: 4,742 Under the null hypothesis Ho, the test statistic is given by (xi-x2) Z= S, 2 Sol + PI nz (9 1.42-83.50) 50.63 136.36 52 53 7.9154 4-2031

Z = 4.203 The p-value of Z-score cat 0:0® 1 sigruficance level IS 0.0000132 the Since p-value <0.001 reject the null bypothesis at v8 01 significance level and conclude that First population mean is greater than second population That is Sample data support the claim that Frost population megn is greater than the second population. mean: is