Consider the following problem that tests a hypothesis:
A random sample of 600 teens with Facebook profiles found that 395 included photos of themselves. Let
be the proportion of teen Facebook users who included photos of themselves a profile pictures.
At significance level , is the sample showing strong evidence that is less than 0.7 ? Use 4
decimal places for .
NO
YES
Note: Round any -score to 2 decimal places before any calculation.

Ask by Mccoy Boyd. in the United States

Mar 21,2025

Question

Consider the following problem that tests a hypothesis:
A random sample of 600 teens with Facebook profiles found that 395 included photos of themselves. Let
be the proportion of teen Facebook users who included photos of themselves a profile pictures.
At significance level , is the sample showing strong evidence that is less than 0.7 ? Use 4
decimal places for .
NO
YES
Note: Round any -score to 2 decimal places before any calculation.

Ask by Mccoy Boyd. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

**Step 1. Define the hypotheses**

We are testing
$$
H_0: p = 0.7 \quad \text{vs} \quad H_a: p < 0.7.
$$

**Step 2. Compute the sample proportion**

The sample proportion is
$$
\hat{p} = \frac{395}{600} \approx 0.6583.
$$

**Step 3. Compute the standard error**

Under the null hypothesis where $$ p = 0.7 $$, the standard error (using $$ n = 600 $$) is
$$
\sigma_{\hat{p}} = \sqrt{\frac{0.7 \times 0.3}{600}} = \sqrt{\frac{0.21}{600}} = \sqrt{0.00035} \approx 0.0187.
$$

**Step 4. Calculate the test statistic**

The test statistic is given by
$$
z = \frac{\hat{p} - 0.7}{\sigma_{\hat{p}}} = \frac{0.6583 - 0.7}{0.0187} \approx \frac{-0.0417}{0.0187} \approx -2.23.
$$

(Round $$ z $$ to 2 decimal places as instructed.)

**Step 5. Compute the $$ p $$-value**

Since this is a left-tailed test, the $$ p $$-value is
$$
P(Z < -2.23) \approx 0.0129.
$$

**Step 6. Make the decision**

The significance level is $$ \alpha = 0.009 $$. Because the $$ p $$-value $$ (0.0129) $$ is greater than $$ 0.009 $$, we do not reject $$ H_0 $$.

**Conclusion**

There is not sufficient evidence to conclude that $$ p < 0.7 $$.

The correct answer is: NO.
There is not enough evidence to say that the proportion of teens with profile pictures is less than 0.7.

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