Question

Asked Dec 7, 2019

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A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. A recent sample of 1,000 adults showed 410 indicating that their financial security was more than fair. Suppose that just a year before, a sample of 1,200 adults showed 420 indicating that their financial security was more than fair.

(a)

State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. (Let *p*_{1} = population proportion most recently saying financial security more than fair and *p*_{2} = population proportion from the year before saying financial security more than fair. Enter != for ≠ as needed.)

p1−p2=0

p1−p2!=0

(b)

Conduct the hypothesis test and compute the *p*-value. At a 0.05 level of significance, what is your conclusion?

Find the value of the test statistic. (Use

p_{1} − p_{2}.

Round your answer to two decimal places.)Find the *p*-value. (Round your answer to four decimal places.)

State your conclusion.

Reject *H*_{0}. There is sufficient evidence to conclude the population proportions are not equal. The data suggest that there has been a change in the population proportion saying that their financial security is more than fair.Do not reject *H*_{0}. There is insufficient evidence to conclude the population proportions are not equal. The data do not suggest that there has been a change in the population proportion saying that their financial security is more than fair. Reject *H*_{0}. There is insufficient evidence to conclude the population proportions are not equal. The data do not suggest that there has been a change in the population proportion saying that their financial security is more than fair.Do not reject *H*_{0}. There is sufficient evidence to conclude the population proportions are not equal. The data suggest that there has been a change in the population proportion saying that their financial security is more than fair.

(c)

What is the 95% confidence interval estimate of the difference between the two population proportions? (Round your answers to four decimal places.)

to

What is your conclusion?

The 95% confidence interval ---Select--- is completely above is completely below contains zero, so we can be 95% confident that the population proportion of adults saying that their financial security is more than fair ---Select--- has increased may have stayed the same has decreased .

Step 1

**a.**

** **

**Null Hypothesis:**

*H*_{0}:*p*_{1}=*p*_{2}

**Alternative Hypothesis:**

*H*_{a}:*p*_{1}-*p*_{2}≠0

**Test Statistic:**

From the given information, *n*_{1}=1000, *x*_{1}=410, *n*_{2}=1200 and *x*_{2}=420.

The pooled sample proportion is,

Step 2

The test statistic is ** 2.89** and it is calculated below:

Step 3

*p***-value:**

The *p*-value is **0.0000** and it is calculated below:

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