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Math  /  Data & Statistics

QuestionPart 1 of 4 Points: 0 of 1 Save
A poll of 1130 teens aged 13 to 17 showed that 53%53 \% of them have made new friends online. Use a 0.01 significance level to test the claim that half of all teens have made new friends online. Use the P -value method. Use the normal distribution as an approximation to the binomial distribution.
Let pp denote the population proportion of all teens aged 13 to 17 who have made new friends online. Identify the null and alternative hypotheses. H0:pYH1:pY□\begin{array}{l|l} \mathrm{H}_{0}: \mathrm{p} & \mathbf{Y} \\ \mathrm{H}_{1}: \mathrm{p} & \mathbf{Y} \\ \square \end{array} (Type integers or decimals. Do not round.)

Studdy Solution

STEP 1

1. The sample size is n=1130 n = 1130 .
2. The sample proportion is p^=0.53 \hat{p} = 0.53 .
3. We are testing the claim that half of all teens have made new friends online, so the hypothesized population proportion is p0=0.50 p_0 = 0.50 .
4. The significance level is α=0.01 \alpha = 0.01 .

STEP 2

1. Define the null hypothesis (H0 H_0 ).
2. Define the alternative hypothesis (H1 H_1 ).

STEP 3

Define the null hypothesis (H0 H_0 ):
The null hypothesis states that the population proportion of teens who have made new friends online is equal to 0.50.
H0:p=0.50 H_0: p = 0.50

STEP 4

Define the alternative hypothesis (H1 H_1 ):
The alternative hypothesis states that the population proportion of teens who have made new friends online is not equal to 0.50.
H1:p≠0.50 H_1: p \neq 0.50
The null and alternative hypotheses are:
H0:p=0.50H1:p≠0.50\begin{array}{l|l} \mathrm{H}_{0}: \mathrm{p} = 0.50 \\ \mathrm{H}_{1}: \mathrm{p} \neq 0.50 \\ \end{array}

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