Existing research states that the proportion of households in a city owning a computer is 30%. However, a local politician believes that that number is wrong. He randomly selects 200 families and finds that 68 of them have computers. Please conduct a formal hypothesis test to verify if the politician’s claim is credible. Select one:
a. H0: p = 0.3, HA: p ≠ 0.3, z = 1.23, p-value = 0.2187, so we conclude there is insufficient evidence for the politician’s claim and fail to reject the null hypothesis.
b. H0: p = 0.3, HA: p > 0.3, z = 1.23, p-value = 0.1093, so we conclude there is insufficient evidence for the politician’s claim and reject the null hypothesis.
c. H0: p = 0.3, HA: p < 0.3, z = 1.23, p-value = 0.8907, so we conclude that there is evidence for the politician’s claim and reject the null hypothesis.
d. H0: p = 0.3, HA: p ≠ 0.3, z = 1.23, p-value = 0.2187, so we conclude that there is evidence for the politician’s claim and reject the null hypothesis.

Now we can calculate the p value as:

And the best conclusion would be:

a. H0: p = 0.3, HA: p ≠ 0.3, z = 1.23, p-value = 0.2187, so we conclude there is insufficient evidence for the politician’s claim and fail to reject the null hypothesis.

Step-by-step explanation:

Information given

n=200 represent the random sample taken

X=68 represent the number of families with computers

estimated proportion of families with computers

is the value to verify

z would represent the statistic

represent the p value

Hypothesis to test

We want to check if the true proportion is equal to 0.3 or not.:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

(1)  

Replacing we got:

Now we can calculate the p value as:

And the best conclusion would be:

a. H0: p = 0.3, HA: p ≠ 0.3, z = 1.23, p-value = 0.2187, so we conclude there is insufficient evidence for the politician’s claim and fail to reject the null hypothesis.

5

step-by-step explanation:

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.