In 1960, census results indicated that the age at which men in a certain region first married had a mean of 24.2 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased since then. Complete parts a through f below. a) Write appropriate hypotheses. Ho: u=24.2 HA: H>24.2 b) We plan to test our hypothesis by selecting a random sample of 40 men who married for the first time last year. Do you think the necessary assumptions for inference are satisfied? Explain. The independence condition should be satisfied and the Nearly Normal Condition should be satisfied because the sample size is large. should be reliable. Therefore, using the Student-t model for inference c) Describe the approximate sampling distribution model for the mean age in such samples. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers, using radicals as needed.) A. t distribution with w degrees of freedom with Mean = 24.2 and SE (y) = √40 B. Normal distribution with Mean = and SE (y) = OC. t distribution with degrees of freedom with Mean = and SE (y) = s d) The men in our sample married at an average age of 25.1 years, with a standard deviation of 5.3 years. That results in a t-statistic of 1.074. What is the P-value for this?
In 1960, census results indicated that the age at which men in a certain region first married had a mean of 24.2 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased since then. Complete parts a through f below. a) Write appropriate hypotheses. Ho: u=24.2 HA: H>24.2 b) We plan to test our hypothesis by selecting a random sample of 40 men who married for the first time last year. Do you think the necessary assumptions for inference are satisfied? Explain. The independence condition should be satisfied and the Nearly Normal Condition should be satisfied because the sample size is large. should be reliable. Therefore, using the Student-t model for inference c) Describe the approximate sampling distribution model for the mean age in such samples. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers, using radicals as needed.) A. t distribution with w degrees of freedom with Mean = 24.2 and SE (y) = √40 B. Normal distribution with Mean = and SE (y) = OC. t distribution with degrees of freedom with Mean = and SE (y) = s d) The men in our sample married at an average age of 25.1 years, with a standard deviation of 5.3 years. That results in a t-statistic of 1.074. What is the P-value for this?
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:d) The men in our sample married at an average age of 25.1 years, with a standard deviation of 5.3 years. That results in a t-statistic of 1.074. What is the P-value for this?
The P-value is w
(Round to three decimal places as needed.)
e) Explain (in context) what this P-value means.
The P-value is the probability of getting a sample mean of 25.1 or older from natural sampling variation given that the null hypothesis is true.
f) What is your conclusion? Use α = 0.05.
Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean age of first marriage is
greater than
the mean age in 1960.
Transcribed Image Text:In 1960, census results indicated that the age at which men in a certain region first married had a mean of 24.2 years. It is widely suspected that young people today are waiting longer to get married. We want to find
out if the mean age of first marriage has increased since then. Complete parts a through f below.
a) Write appropriate hypotheses.
Ho: μ = 24.2
HA: H>24.2
b) We plan to test our hypothesis by selecting a random sample of 40 men who married for the first time last year. Do you think the necessary assumptions for inference are satisfied? Explain.
The independence condition should be satisfied and the Nearly Normal Condition should be satisfied because the sample size is large.
should be reliable.
Therefore, using the Student-t model for inference
c) Describe the approximate sampling distribution model for the mean age in such samples. Select the correct choice below and fill in the answer boxes to complete your choice.
(Type exact answers, using radicals as needed.)
A. t distribution with w degrees of freedom with Mean = 24.2 and SE (y)
=
B. Normal distribution with Mean = and SE (y)
C. t distribution with
S
degrees of freedom with Mean =
√40
and SE (y) =S
d) The men in our sample married at an average age of 25.1 years, with a standard deviation of 5.3 years. That results in a t-statistic of 1.074. What is the P-value for this?
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