Sure, here is the transcription of the text from the image:---After you calculate the p-value, state and justify your decision.- ○ Accept \( H_0 \) because the p-value > α.- ○ Reject \( H_0 \) because the p-value > α.- ○ Accept \( H_0 \) because the p-value < α.- ○ Reject \( H_0 \) because the p-value < α.- ○ Fail to reject \( H_0 \) because the p-value < α.- ○ Fail to reject \( H_0 \) because the p-value > α.---The correct conclusion is that we [Select an answer] conclude that the average number of date nights [Select an answer] married men without children initiate [Select an answer] days.---What level of concern do you have for the validity of your results?- ○ Valid — the sample size is greater than 30- ○ Questionable — there is likely to be some response bias, but at least \( n > 30 \)- ○ Questionable — there is likely to be some nonresponse bias, but at least \( n > 30 \)- ○ Questionable — there is likely to be some nonresponse bias and, while \( n > 30 \), the skewness in the distribution is concerning- ○ Questionable — While \( n > 30 \), the skewness in the distribution is concerning- ○ Questionable — there is likely to be some response bias and, while \( n > 30 \), the skewness in the distribution is concerning--- **Hypothesis Testing on Date Nights Initiation****Scenario:**Forty married couples without children are surveyed on the number of times per year they initiate a date night. The men report an average of 7.5 date nights with a standard deviation of 4.7. We are tasked to assess if there is significant evidence that married men without children initiate date nights at least 6 times per year at the 0.05 significance level. Note that the distribution is skewed.**Questions:**1. **What are the hypotheses?** - \( H_0: \mu \leq 6 \) vs \( H_1: \mu > 6 \) - \( H_0: \mu = 7.5 \) vs \( H_1: \mu \neq 7.5 \) - \( H_0: \mu = 6 \) vs \( H_1: \mu \neq 6 \) - \( H_0: \mu \leq 7.5 \) vs \( H_1: \mu > 7.5 \)2. **What distribution does the test statistic follow?** - \( t \) with 40 degrees of freedom - \( t \) with 39 degrees of freedom - \( t \) with 41 degrees of freedom - \( z \)3. **What is the value of the test statistic?** *Round to two decimal places.*4. **What is the probability statement for the p-value?** - \( P(T \geq \text{test statistic}) \) - \( P(Z \geq \text{test statistic}) \) - \( 2P(Z \neq \text{test statistic}) \) - \( 2P(T \neq \text{test statistic}) \) - None of the above5. **After you calculate the p-value, state and justify your decision.**This exercise involves setting up hypotheses, determining the correct statistical test and distribution, computing test statistics, and concluding based on p-values.

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Description: Sure, here is the transcription of the text from the image:---After you calculate the p-value, state and justify your decision.- ○ Accept \( H_0 \) because the p-value > α.- ○ Reject \( H_0 \) because the p-value > α.- ○ Accept \( H_0 \) because the

Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved. Let μ denotes the population mean men report initiating. The hypothesis is, Null hypothesis: H0:μ=6 Alternative hypothesis: H1:μ≠6 Correct Answer: Option H0:μ=6 vs H1:μ≠6. It is clear that the population standard deviation is unknown indicating that the test statistic follows t with 39=n-1 degrees of freedom. Correct Answer: Option t with 39 degrees of freedom.The value of test statistic is, t=x¯-μsn=7.5-64.740=1.50.7431=2.02 Thus, the test statistic value is 2.02.

Math

Statistics

40 married couples without children are asked to report the number of times per year they initiate a date night. The men report initiating an average of 7.5 date nights with a standard deviation of 4.7. Is there significant evidence to conclude that married men without children initiate date night 6 times per year at the 0.05 significance level? Note that there's evidence that this distribution is skewed. What are the hypotheses? Ho: µ < 6 vs Hị: µ > 6 Ho: µ = 7.5 vs H1: µ # 7.5 Ho: μ= 6 νs Ηi: μ 6 Ο Η: μ < 7.5 vs Η1: μ > 7.5 What distribution does the test statistic follow? Ot with 40 degrees of freedom Ot with 39 degrees of freedom t with 41 degrees of freedom What is the value of the test statistic? Round to two decimal places.

40 married couples without children are asked to report the number of times per year they initiate a date night. The men report initiating an average of 7.5 date nights with a standard deviation of 4.7. Is there significant evidence to conclude that married men without children initiate date night 6 times per year at the 0.05 significance level? Note that there's evidence that this distribution is skewed. What are the hypotheses? Ho: µ < 6 vs Hị: µ > 6 Ho: µ = 7.5 vs H1: µ # 7.5 Ho: μ= 6 νs Ηi: μ 6 Ο Η: μ < 7.5 vs Η1: μ > 7.5 What distribution does the test statistic follow? Ot with 40 degrees of freedom Ot with 39 degrees of freedom t with 41 degrees of freedom What is the value of the test statistic? Round to two decimal places.

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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