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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman