Multiple Choice
A teacher claims her students’ average test score is 75. A researcher suspects it’s different. A sample of 25 students has a mean score of 78 with a standard deviation of 6.
At the significance level, test the claim.
9. Hypothesis Testing for One Sample
Link Between Confidence Intervals and Hypothesis Testing
Multiple Choice
A teacher claims her students’ average test score is 75. A researcher suspects it’s different. A sample of 25 students has a mean score of 78 with a standard deviation of 6.
Create a confidence interval for the mean test score.
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Verified step by step guidance1
Identify the sample statistics: sample mean \( \bar{x} = 78 \), sample standard deviation \( s = 6 \), and sample size \( n = 25 \).
Since the population standard deviation is unknown and the sample size is small (less than 30), use the t-distribution to construct the confidence interval.
Determine the degrees of freedom \( df = n - 1 = 24 \) and find the critical t-value \( t^* \) corresponding to a 90% confidence level and 24 degrees of freedom from the t-table or statistical software.
Calculate the standard error of the mean using the formula:
\( SE = \frac{s}{\sqrt{n}} \)
Construct the confidence interval using the formula:
\( \left[ \bar{x} - t^* \times SE, \ \bar{x} + t^* \times SE \right] \)
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