Math / Data & Statistics

Questionssignment 30: Test 5 Review Khadijah Daley 11/18/24 3:07 PM Question 10, 8.2.15-T HW Score: 49.84\%, 14.95 of 30 points Part 1 of 4 Points: 0 of 1 Save
A poll of 1160 Americans showed that $47.1 \%$ of the respondents prefer to watch the news rather than read or listen to it. Use those results with a 0.10 significance level to test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it. Use the P -value method. Use the normal distribution as an approximation to the binomial distribution.
Let $p$ denote the population proportion of all Americans who prefer to watch the news rather than read or listen to it. Identify the null and alternative hypotheses. $\begin{array}{l|l} \mathrm{H}_{0}: \mathrm{p} & \mathrm{~V} \\ \mathrm{H}_{1}: \mathrm{p} & \mathrm{~V} \\ \hline \end{array}$ (Type integers or decimals. Do not round.)

Studdy Solution

STEP 1

1. We are testing a claim about the population proportion $p$ .
2. The sample size is 1160 Americans.
3. The sample proportion is $47.1\%$ or $0.471$ .
4. We are using a significance level of $\alpha = 0.10$ .
5. The normal distribution is used as an approximation to the binomial distribution.

STEP 2

1. Define the null and alternative hypotheses.
2. Calculate the test statistic.
3. Determine the P-value.
4. Compare the P-value with the significance level to make a decision.

STEP 3

Define the null hypothesis ( $H_0$ ) and the alternative hypothesis ( $H_1$ ).
- The null hypothesis ( $H_0$ ) states that the population proportion $p$ is equal to 0.5, i.e., half of Americans prefer to watch the news. - The alternative hypothesis ( $H_1$ ) states that the population proportion $p$ is less than 0.5, i.e., fewer than half of Americans prefer to watch the news.
$\begin{array}{l|l} \mathrm{H}_{0}: \mathrm{p} & = 0.5 \\ \mathrm{H}_{1}: \mathrm{p} & < 0.5 \\ \hline \end{array}$
The null and alternative hypotheses are identified as:
$\begin{array}{l|l} \mathrm{H}_{0}: \mathrm{p} & = 0.5 \\ \mathrm{H}_{1}: \mathrm{p} & < 0.5 \\ \hline \end{array}$

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