Question

Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.49 A newspaper article states that only a minority of the Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey as evidence. Conduct a hypothesis test to determine if these data provide strong evidence supporting this statement using the 7 steps and a significance level of 0.05.

Answer 1

Answer:

Step-by-step explanation:

We want to test hypothesis:

$H_0 : p\geq0.5$

$H_a : p < 0.5$

This is a lower tailed test

Sample proportion. $\stackrel{\wedge}{p}$=0.48, n= 331

And claimed proportion, P=0.5

Significance level, α=0.05  (if no value is given, we take level of 0.05)

Now, calculating statistics

Standard deviation of $\stackrel{\wedge}{p}$,$\sigma_{\stackrel{\wedge}{p}}$ = $\frac{\sqrt{P*(1-P)}}{n}$

= $\frac{\sqrt{0.05*(1-0.05)}}{331}$

 $\approx$0.0275

Test statistic,$z_{observed }$= $\frac{(\stackrel{\wedge}{p}-0.5)}{ \sigma_{\stackrel{\wedge}{p}}}$

=$\frac{ ((0.48)-0.5)}{0.0275}$

$\approx$ -0.727736

$\approx$  -0.73

Test statistic: -0.73

Since this is lower tailed test, p value = $P(Z < z_{observed})$= P ( Z < -0.73) = 0.2327

p-value= 0.2327

note that exact p-value is : 0.2333875382

Rejection criteria : reject H0 if p-value < $\alpha$

Decision: Since$p-value\geq\alpha$, we fail to reject the null hypothesis. There is insufficient evidence to conclude that p is less than 0.5

Alternatively, we can use critical value approach,

$Z_c= -z_\alpha=-z_{0.05}=-z_{0.05}=-1.645$(From z table, using interpolation, ½th distance between -1.64 and -1.65)

critical value = -1.645

Rejection criteria: Reject$H_0$ if $z_0< -1.645$

Decision : since $z_o \geq z_c$, we fail to reject the null hypothesis. There is insufficient evidence to conclude that p is less than to 0.5

Answer 2

The conclusion about the hypothesis test to provide evidence for the given statements;  strong evidence supporting the statement that only a minority of the Americans who decide not to go to college do so because they cannot afford it

How to conduct a Hypothesis Testing?

• Step 1:

Let us state the Null hypothesis;

Null Hypothesis; H0: p = 0.5

• Step 2;

Let us state the Alternative Hypothesis;

Alternative Hypothesis; Ha: p < 0.5

• Step 3; Let us set the decision rule;

Critical value at α = 0.05 is 1.645. Thus, the decision rule is to reject the null hypothesis if the test statistic is less than -1.645 since it's a left tailed test.

• Step 4; Find the parameters;

Standard deviation is; s = √(p(1 - p)/n)

s = √(0.5(1 - 0.5)/331)

s = 0.0275

sample proportion; p^ = 0.48

population proportion; p = 0.5

• Step 5; Find the test statistic

Formula for the test statistic is gotten from the formula;

z = (p^ - p)/s

z = (0.48 - 0.5)/0.0275

z = -0.728

Step 6; Set the acceptance/rejection region;

The z-value is greater than the critical value and so we will reject the null hypothesis.

Step 7: Since we fail to reject the null hypothesis, we will conclude that the data provides strong evidence supporting the statement that only a minority of the Americans who decide not to go to college do so because they cannot afford it

Read more about creating hypothesis at; https://brainly.com/question/15980493