Question

Two independent samples have been selected, 6262 observations from population 1 and 5151 observations from population 2. The sample means have been calculated to be x¯¯¯1=13.2x¯1=13.2 and x¯¯¯2=11.5x¯2=11.5. From previous experience with these populations, it is known that the variances are σ21=39σ12=39 and σ22=29σ22=29.For the hypothesis test of H0:(μ1−μ2)=1.6H0:(μ1−μ2)=1.6 and Ha:(μ1−μ2)≠1.6Ha:(μ1−μ2)≠1.6 Use α=0.04α=0.04.(a) Compute the test statistic.z=z=(b) Find the approximate p-valuep−value=p−value=The final conclustion isA. There is not sufficient evidence to reject the null hypothesis that (μ1−μ2)=1.6(μ1−μ2)=1.6.B. We can reject the null hypothesis that (μ1−μ2)=1.6(μ1−μ2)=1.6 and accept that (μ1−μ2)≠1.6(μ1−μ2)≠1.6.

Answer 1

a) The test statistic for the two independent samples is 0.7

b) The p-value for the test sample is 0.483 , here p-value is greater than significance level.Thus, there is no sufficient evidence to reject null hypothesis.

Given,

significance level, \alpha = 0.04

From population 1,

Mean, $x_1=13.2$

variance, $\sigma^2_1=39$

standard deviation, $\sigma_1 =6.24$

sample size,$n_1=62$

From population 2,

Mean, $x_2=11.5$

variance, $\sigma^2_2 = 29$

standard deviation, $\sigma_2=4.47$

Test hypothesis,

$H_0:(\mu_1-\mu_2)=1.6\\\\H_a:(\mu_1-\mu_2)\neq1.6$

a)

The test statistic can be determined by formula,

$z=\frac{(x_1-x_2)-d}{\sqrt{\frac{S^2_1}{n^2_1}+\frac{S^2_2}{n_2}}}$

$d=\mu_1-\mu_2=1.6$

$z=\frac{(13.2-11.5)-1.6}{\sqrt{\frac{6.24^2}{62^2}+\frac{4.47^2}{51}}}\\\\z=\frac{0.1}{\sqrt{0.01+0.007}}\\\\z=\frac{0.1}{0.13}=0.7$

b)

P-value can be calculated by the z-score table

as z=0.7 then from z-value table

p=0.483

A p-value greater than 0.04 (> 0.04) indicates strong support for the null hypothesis. This means that the null hypothesis is retained and the alternative hypothesis is rejected. It is important to note that you cannot accept the null hypothesis; we can only reject it or fail to reject it.

To learn more about test statistic refer here

https://brainly.com/question/14128303

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