Question
An educator estimates that the dropout rate for seniors at high schools in Istanbul is 15%. Last year, 38 seniors from a random sample of 200 Istanbul seniors withdrew. At α=0.05, is there enough evidence to reject the educator’s claim?
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Answer to a math question An educator estimates that the dropout rate for seniors at high schools in Istanbul is 15%. Last year, 38 seniors from a random sample of 200 Istanbul seniors withdrew. At α=0.05, is there enough evidence to reject the educator’s claim?
Andrea
4.575 Answers
1. Formulate the hypotheses:
H_0 : p = 0.15
H_a : p \neq 0.15
2. Calculate the sample proportion:
\hat{p} = \frac{38}{200} = 0.19
3. Determine the sample size and significance level:
n = 200
\alpha = 0.05
4. Compute the test statistic:
z=\frac{\hat{p} - p_0}{\sqrt{\frac{p_0 \times(1 - p_0)}{n}}}=\frac{0.19 - 0.15}{\sqrt{\frac{0.15 \times(1 - 0.15)}{200}}}\approx1.58
5. Determine the p-value:
P(z)=2\times P(Z>1.58)\approx2\times0.05705=0.1141
Since the p-value is greater than the significance level (0.1141 > 0.05), we do not reject the null hypothesis.
Answer: There is not enough evidence to reject the educator’s claim.
2. Calculate the sample proportion:
3. Determine the sample size and significance level:
4. Compute the test statistic:
5. Determine the p-value:
Since the p-value is greater than the significance level (0.1141 > 0.05), we do not reject the null hypothesis.
Answer: There is not enough evidence to reject the educator’s claim.
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