Question

This Test: 19 pts pos Question Help Is the difference between the mean annual salaries of statisticians in Region 1 and Region 2 more than $4000? To decide, you select a random sample of statisticians from each region. The results of each survey are shown to the right Al a0.10, what should you conclude? Region 1 Region 2 2- $58,000 2- $9150 Click here to view page 1 of the standard Click here to view page 2 of the standard normal distribution table normal distribution table Choose the correct nul and alternative hypotheses below O A. Ho P- 4000 H 25 4000 OB. Ho P-H > 4000 H -2 4000 OC. H H-P, s4000 H H > 4000 OF. H H - + 4000 H, 4000 OD. H H -2 = 4000 H - 4000 OE. H -2 4000 H, -< 4000 Determine the critical value(s). Click to select your answer(s)

Answer 1

Let $\mu_1$ be the true average annual salary of statisticians in region 1 and $\mu_2$ be the true average annual salary of statisticians in region 2.

We want to test if the difference between the the mean annual salary of statisticians in region 1 and region 2 is more than $4000. That is, we want to test if This would be the alternative hypothesis as the alternative hypothesis always has an inequality.

H1 - H2> 4000

The null and alternative hypotheses are

ans:

Ос. % - дооо на B-2 > 4000

The significance level to test the hypotheses is

a = 0.1

This is a 1 tailed (right tail) test (the alternative hypothesis has ">")

The sample sizes of both the samples are greater than 30 and hence using the central limit theorem, we can say that the sampling distribution of the difference in mean is normal.

The right tail critical value is

P(Z > Za) = a = 0.1 P (Z < 2) = 1-0.1 = 0.90 S

Using the standard normal tables we can get for z=1.28, P(Z<1.28) = 0.90

Hence the right tail critical value is

Za = 1.28

ans:

20 = 1.28

Since this is a right tailed test, we will reject the null hypothesis if the test statistic is greater than the critical value.

Hence the rejection region is

ans: B. z>1.28

We have the following sample information

T1 = 67900 01 = 8775 nu = 48 T2 = 58000 02 = 9150 n2 = 43

The standard error of the difference in means is

031-19 = 1 + 0 = /37752 , 91502 V nang 48 +43 = 1884.4667

The hypothesized value of the difference between the means is (from the null hypothesis)

(μι - μ2)Η, = 4000

The test statistic is

(@1 - 12) - (M1 - M2), (67900 - 58000) – 4000 1884.4667 = 3.13 011-12

ans: The standardized test statistic for is

11 - 12

z=3.13

We will reject the null hypothesis if the test statistic lies in the rejection region. Here, the test statistic is 3.13 and it lies in the rejection region >1.28.

Hence we reject the null hypothesis.

ans:

O A Reject H, Al the 10% significance level there is sufficient evidence to support the claim that the difference between the mean annual salaries is more than 50000