Mathematics, 15.04.2020 21:37 noslengerman

A personnel director in a particular state claims that the mean annual income is the same in one of the state's counties (County A) as it is in another county (County B). In County A, a random sample of 18 residents has a mean annual income of $ 40 comma 400 and a standard deviation of $ 8700. In County B, a random sample of 8 residents has a mean annual income of $ 39 comma 200 and a standard deviation of $ 6000. At alphaequals0.10, answer parts (a) through (e). Assume the population variances are not equal. Assume the samples are random and independent, and the populations are normally distributed.

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a) The hypothesis that the mean annual income is the same could not be rejected. There is no enough evidence to claim they are different.

b) The critical values for this two-sided test are t=±1.711.

Step-by-step explanation:

The question is incomplete:

(a) Identify the claim and state H0 and Ha.

Which is the correct claim below?

(b) Find the critical value(s) and identify the rejection region(s).

Enter the critical value(s) below.

We have an hypothesis test on the difference of two means.

The null and alternative hypothesis are:

$H_0: \mu_a-\mu_b=0\\\\H_a: \mu_a-\mu_b\neq 0$

The claim of the alternative hypothesis is that the mean annual income is different in County A and County B.

The null hypothesis is that the mean annual income is equal in both counties.

The significance level is α=0.10.

The sample from County A has a mean of S40,400, a s.d. of $8,700 and a sample size of 18 residents.

The sample from County B has a mean of S39,200, a s.d. of $6,000 and a sample size of 8 residents.

The standard error of the difference of means is:

$\sigma_d=\sqrt{\frac{\sigma_a^2}{n_a}+\frac{\sigma_b^2}{n_b}}=\sqrt{\frac{8700^2}{18}+\frac{6000^2}{8}}=\sqrt{8705000}=2950$

The degrees of freedom are:

df=n_a+n_b-2=18+8-2=24

Then, the test statistic is:

$t=\frac{\Delta M-\Delta \mu}{\sigma_d} =\frac{(40,400-39,200)-0}{2950} =\frac{1200}{2950}=0.407$

For a statistic t=0.407, and df=24, the P-value is P=0.69. As the P-value is bigger than the significance level, the null hypothesis failed to be rejected.

If we would use the critial value approach, we would have to calculate the critical values for t, for df=24, two sided test and α=0.10.

The critical values, looking in a table, are t=1.711.

Answer from: Quest

f(x) is the value of the function. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane.

step-by-step explanation:

hope this !

Answer from: Quest

the answer for this question is : 360°

step-by-step explanation:

we have been given a triangle we need to tell which one of these is a triangle below to map onto itself.

360° rotation is the complete rotation which eventually leads to the same figure which is given.

the correct will be, that is 360° that will cause the triangle below to map onto itself.

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