A development economist is studying income growth in a rural area of a developing country. The last census of the population of this area, several years earlier, showed that mean household annual income was 425 dollars, and the variance of household income was 2500 (dollarssquared). A current random sample of 100 households yields a sample mean income of $433.75. Assume that household annual incomes are approximately normally distributed, and that the population variance is known still to be 2500. Test the null hypothesis that population mean income has not increased ( H0 : "m"(greek letter) greater than equal to< 425 ) against the alternative hypothesis that it has increased ( HA :"m"(greek letter > 425 ), at a 1% level of significance. What is the form of the rejection region?
a. Reject H0 if x < cv
b. Reject H0 if x > cv
c. Reject H0 if x < cv or if x > cv
d. Reject H0 if x = cv 3
What is the critical value?
a. 436.63
b. 433.75
c. 425
d. 437.88
What is the conclusion of the hypothesis test?
a. Accept H0
b. Reject H0 in favor of HA

Reject H0 if x > cv

Step-by-step explanation:

The hypothesis :

H0 : μ ≤ 425

H1 : μ > 425

Standard deviation, s = √2500 = 50

Sample size, n = 100

xbar = 433.5

The test statistic, Z :

(xbar - μ) / s/√n

(433.5 - 425) / 50/10

Z = 8.5 / 5 = 1.7

The decision region ;

|Z| > Z0.01 ; Reject H0

From Z table ;critical value, Z0.01 = 2.33

1.7 < 2.33 ; We fail to reject then Null and conclude that thee is no significant evidence support the claim that population mean income has increased.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

if you are saying purchasing 3 social media ads and one newspaper ad counts as one purchase then there are:

6 purchases

if you are asking how many of each then:

18 social media ads

6 newspaper ads