A college professor claims that the entering class this year appears to be smarter than entering classes from previous years. He tests a random sample of 20 this year's entering students and finds that their mean IQ score is 117, with standard deviation of 15. The college records indicate that the mean IQ score for entering students from previous years is 113. If we assume that the IQ scores of this year's entering class are normally distributed, is there enough evidence conclude, at the 0.05 level of significance, that the mean IQ score, μ, of this year's class is greater than that of previous years? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) 4 (a) State the null hypothesis Ho and the alternative hypothesis H₁. H: H = 113 H :μ > 113 (b) Determine the type of test statistic to use. Degrees of freedom: 19 (c) Find the value of the test statistic. (Round to three or more decimal places.) 1.193 (d) Find the p-value. (Round to three or more decimal places.) 0.124 (e) Can we conclude, using the 0.05 level of significance, that the mean IQ score Fulanation Check 3 Ix X 09 0-0 a X S O=O OSO 00 O 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Prive
A college professor claims that the entering class this year appears to be smarter than entering classes from previous years. He tests a random sample of 20 this year's entering students and finds that their mean IQ score is 117, with standard deviation of 15. The college records indicate that the mean IQ score for entering students from previous years is 113. If we assume that the IQ scores of this year's entering class are normally distributed, is there enough evidence conclude, at the 0.05 level of significance, that the mean IQ score, μ, of this year's class is greater than that of previous years? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) 4 (a) State the null hypothesis Ho and the alternative hypothesis H₁. H: H = 113 H :μ > 113 (b) Determine the type of test statistic to use. Degrees of freedom: 19 (c) Find the value of the test statistic. (Round to three or more decimal places.) 1.193 (d) Find the p-value. (Round to three or more decimal places.) 0.124 (e) Can we conclude, using the 0.05 level of significance, that the mean IQ score Fulanation Check 3 Ix X 09 0-0 a X S O=O OSO 00 O 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Prive
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Hypothesis Test for the Population Mean: t Test**
A college professor claims that the entering class this year is smarter than previous years. A random sample of 20 students from this year's entering students shows a mean IQ score of 117, with a standard deviation of 15. Historical data indicates that the mean IQ score for previous years was 113. Assuming IQ scores are normally distributed, we want to determine if there is enough evidence to conclude, at the 0.05 level of significance, that the mean IQ score of this year's class is greater than previous years.
Perform a one-tailed test and complete the following:
(a) State the **null hypothesis** \( H_0 \) and the **alternative hypothesis** \( H_1 \):
- \( H_0 : \mu = 113 \)
- \( H_1 : \mu > 113 \)
(b) Determine the type of **test statistic** to use:
- **Test statistic:** t
- **Degrees of freedom:** 19
(c) Find the value of the test statistic:
- Calculated value: 1.193 (rounded to three decimal places)
(d) Find the **p-value**:
- Calculated value: 0.124 (rounded to three decimal places)
(e) Can we conclude, using the 0.05 level of significance, that the mean IQ score of this year's class is greater than that of previous years?
- Based on the p-value, we fail to reject the null hypothesis, indicating insufficient evidence to support the claim that this year's mean IQ score is greater.
> **Explanation:** In hypothesis testing, the null hypothesis represents no effect or difference, while the alternative suggests a deviation. A p-value below 0.05 would indicate significant evidence to reject \( H_0 \) in favor of \( H_1 \). Here, the p-value of 0.124 suggests insufficient evidence against \( H_0 \).
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