A psychologist obtains a random sample of 25 mothers in the first trimester of their pregnancy. The mothers are asked to play classical music 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 know normally distributed with a mean of 100. If the IQs of the 25 children in the study result in a sample mean of 107.5 and sample standard deviation of 16, is there evidence that the children have higher IQs? Use the a=0.01 level of significance. Complete parts (a) th Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). Click here to view the table of critical t-values. (a) Determine the null and alternative hypotheses. H₂ VI H₂ (Type integers (b) Identify the test statistic. decimals. Do not round.) (Round to two decimal places as needed.) Approximate the P-value. The P-value is in the range (c) State the conclusion for the test. O A. Reject H, because the P-value is greater than the a=0.01 level of significance. OB. Reject H, because the P-value is less than the = 0.01 level of significance. OC. Do not reject H, because the P-value is less than the a=0.01 level of significance. O D. Do not reject H, because the P-value is greater than the a=0.01 level of significance. (d) State the conclusion in context of the problem. There sufficient evidence at the a=0.01 level of significance to conclude that mothers who listen classical music have children with higher IQs.
A psychologist obtains a random sample of 25 mothers in the first trimester of their pregnancy. The mothers are asked to play classical music 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 know normally distributed with a mean of 100. If the IQs of the 25 children in the study result in a sample mean of 107.5 and sample standard deviation of 16, is there evidence that the children have higher IQs? Use the a=0.01 level of significance. Complete parts (a) th Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). Click here to view the table of critical t-values. (a) Determine the null and alternative hypotheses. H₂ VI H₂ (Type integers (b) Identify the test statistic. decimals. Do not round.) (Round to two decimal places as needed.) Approximate the P-value. The P-value is in the range (c) State the conclusion for the test. O A. Reject H, because the P-value is greater than the a=0.01 level of significance. OB. Reject H, because the P-value is less than the = 0.01 level of significance. OC. Do not reject H, because the P-value is less than the a=0.01 level of significance. O D. Do not reject H, because the P-value is greater than the a=0.01 level of significance. (d) State the conclusion in context of the problem. There sufficient evidence at the a=0.01 level of significance to conclude that mothers who listen classical music have children with higher IQs.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Transcribed Image Text:A psychologist obtains a random sample of 25 mothers in the first trimester of their pregnancy. The mothers are asked to play classical music 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 25 children in the study result in a sample mean of 107.5 and sample standard deviation of 16, is there evidence that the children have higher IQs? Use the α = 0.01 level of significance. Complete parts (a) through (d).
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
Click here to view the table of critical t-values.
(a) Determine the null and alternative hypotheses.
H₂: ▼
H₂:
▼ ▼
(Type integers or decimals. Do not round.)
(b) Identify the test statistic.
(Round to two decimal places as needed.)
Approximate the P-value.
The P-value is in the range
(c) State the conclusion for the test.
O A. Reject Ho because the P-value is greater than the a= 0.01 level of significance.
O B. Reject Ho because the P-value is less than the α = 0.01 level of significance.
O C. Do not reject Ho because the P-value is less than the x = 0.01 level of significance.
O D. Do not reject Ho because the P-value is greater than the x = 0.01 level of significance.
(d) State the conclusion in context of the problem.
There
(...)
sufficient evidence at the α = 0.01 level of significance to conclude that mothers who listen to classical music have children with higher IQs.
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