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A psychologist obtains a random sample of 20 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 30 minutes each day until they give birth. After 5 years, the child is administered an IQ test. It is known that IQs are normally distributed with a mean of 100. If the IQs of the 20 children in the study result in a sample mean of 104.6 and sample standard deviation of 14.1, is there evidence that the children have higher IQs? Use the a = 0.05 level of significance. Test statistic = 1.46 (Round to two decimal places as needed.) Calculate the P-value. P-value = 0.080 (Round to three decimal places as needed.) State the conclusion for the test. Choose the correct answer below. O A. Do not reject Ho. There is not sufficient evidence at the a = 0.05 level of significance to conclude that mothers who listen to Mozart have children with higher IQs. B. Do not reject Ho. There is sufficient evidence at the a= 0.05 level of significance to conclude that mothers who listen to Mozart have children with lower IQs. OC. Reject Ho. There is not sufficient evidence at the a = 0.05 level of significance to conclude that mothers who listen to Mozart have children with lower IQs. D. Reject Ho. There is sufficient evidence at the a = 0.05 level of significance to conclude that mothers who listen to Mozart have children with higher IQs.

A psychologist obtains a random sample of 20 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 30 minutes each day until they give birth. After 5 years, the child is administered an IQ test. It is known that IQs are normally distributed with a mean of 100. If the IQs of the 20 children in the study result in a sample mean of 104.6 and sample standard deviation of 14.1, is there evidence that the children have higher IQs? Use the a = 0.05 level of significance. Test statistic = 1.46 (Round to two decimal places as needed.) Calculate the P-value. P-value = 0.080 (Round to three decimal places as needed.) State the conclusion for the test. Choose the correct answer below. O A. Do not reject Ho. There is not sufficient evidence at the a = 0.05 level of significance to conclude that mothers who listen to Mozart have children with higher IQs. B. Do not reject Ho. There is sufficient evidence at the a= 0.05 level of significance to conclude that mothers who listen to Mozart have children with lower IQs. OC. Reject Ho. There is not sufficient evidence at the a = 0.05 level of significance to conclude that mothers who listen to Mozart have children with lower IQs. D. Reject Ho. There is sufficient evidence at the a = 0.05 level of significance to conclude that mothers who listen to Mozart have children with higher IQs.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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### Study on the Effect of Music on Child IQ Development A psychologist conducted a study with a random sample of 20 mothers in the first trimester of pregnancy. These mothers were asked to play Mozart for at least 30 minutes daily until childbirth. Five years later, an IQ test was administered to the children. Considering that IQs are usually distributed with a mean of 100, the study recorded a sample mean IQ of 104.6 for the children, with a sample standard deviation of 14.1. The inquiry here is whether there is evidence that these children have higher IQs than the general population. A significance level of α = 0.05 was used for the analysis. - **Test Statistic**: 1.46 (Round to two decimal places as needed.) #### Calculation: - **P-value**: 0.080 (Round to three decimal places as needed.) #### Conclusion: Select the appropriate conclusion based on the significance level: - **A.** Do not reject H₀. There is not sufficient evidence at the α = 0.05 level of significance to conclude that mothers who listen to Mozart have children with higher IQs. - **B.** Do not reject H₀. There is sufficient evidence at the α = 0.05 level of significance to conclude that mothers who listen to Mozart have children with lower IQs. - **C.** Reject H₀. There is not sufficient evidence at the α = 0.05 level of significance to conclude that mothers who listen to Mozart have children with lower IQs. - **D.** Reject H₀. There is sufficient evidence at the α = 0.05 level of significance to conclude that mothers who listen to Mozart have children with higher IQs. **Chosen Answer: A.** This result suggests that the effect of listening to Mozart during pregnancy on child IQ development, in this sample, does not show a statistically significant increase in IQ scores at the 0.05 level.
Transcribed Image Text:### Study on the Effect of Music on Child IQ Development A psychologist conducted a study with a random sample of 20 mothers in the first trimester of pregnancy. These mothers were asked to play Mozart for at least 30 minutes daily until childbirth. Five years later, an IQ test was administered to the children. Considering that IQs are usually distributed with a mean of 100, the study recorded a sample mean IQ of 104.6 for the children, with a sample standard deviation of 14.1. The inquiry here is whether there is evidence that these children have higher IQs than the general population. A significance level of α = 0.05 was used for the analysis. - **Test Statistic**: 1.46 (Round to two decimal places as needed.) #### Calculation: - **P-value**: 0.080 (Round to three decimal places as needed.) #### Conclusion: Select the appropriate conclusion based on the significance level: - **A.** Do not reject H₀. There is not sufficient evidence at the α = 0.05 level of significance to conclude that mothers who listen to Mozart have children with higher IQs. - **B.** Do not reject H₀. There is sufficient evidence at the α = 0.05 level of significance to conclude that mothers who listen to Mozart have children with lower IQs. - **C.** Reject H₀. There is not sufficient evidence at the α = 0.05 level of significance to conclude that mothers who listen to Mozart have children with lower IQs. - **D.** Reject H₀. There is sufficient evidence at the α = 0.05 level of significance to conclude that mothers who listen to Mozart have children with higher IQs. **Chosen Answer: A.** This result suggests that the effect of listening to Mozart during pregnancy on child IQ development, in this sample, does not show a statistically significant increase in IQ scores at the 0.05 level.
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