Question

1-A) Identify the P-VALUE in a hypothesis test of the following claim and sample data:



Claim: “The average weekly number of hours spent studying by students who sit in the front of the classroom is greater than that of students who sit in the back of the classroom.”



Dozens of randomly selected students were asked how many hours they study per week. There were 35 students who said that they tend to sit toward the front of the classroom, and their reported number of study hours per week had a mean of 17.26 and standard deviation of 9.34. There were 36 students who said they tend to sit toward the back of the classroom, and they had a mean of 11.08 and standard deviation of 8.64. The standard deviation for the population of students who sit in the front is assumed to be the same as that for those who sit in the back. Test the claim at the 0.01 significance level.

a.	5.664×10-13	b.	0.0026
c.	4.155×10-21	d.	0.0025

B)  

Identify the value of the CRITICAL VALUE(S) used in a hypothesis test of the following claim and sample data:



Claim: “The average weekly number of hours spent studying by students who sit in the front of the classroom is greater than that of students who sit in the back of the classroom.”



Dozens of randomly selected students were asked how many hours they study per week. There were 35 students who said that they tend to sit toward the front of the classroom, and their reported number of study hours per week had a mean of 17.26 and standard deviation of 9.34. There were 36 students who said they tend to sit toward the back of the classroom, and they had a mean of 11.08 and standard deviation of 8.64. The standard deviation for the population of students who sit in the front is assumed to be the same as that for those who sit in the back. Test the claim at the 0.01 significance level.

a.	2.33	b.	2.382
c.	2.441	d.	2.438

C)

Claim: “The average weekly number of hours spent studying by students who sit in the front of the classroom is greater than that of students who sit in the back of the classroom.”



Dozens of randomly selected students were asked how many hours they study per week. There were 35 students who said that they tend to sit toward the front of the classroom, and their reported number of study hours per week had a mean of 17.26 and standard deviation of 9.34. There were 36 students who said they tend to sit toward the back of the classroom, and they had a mean of 11.08 and standard deviation of 8.64. The standard deviation for the population of students who sit in the front is assumed to be the same as that for those who sit in the back. Test the claim at the 0.01 significance level.

a.	2.895	b.	13.281
c.	2.892	d.	10.933

D)  

Claim: “The average weekly number of hours spent studying by students who sit in the front of the classroom is greater than that of students who sit in the back of the classroom.”



Dozens of randomly selected students were asked how many hours they study per week. There were 35 students who said that they tend to sit toward the front of the classroom, and their reported number of study hours per week had a mean of 17.26 and standard deviation of 9.34. There were 36 students who said they tend to sit toward the back of the classroom, and they had a mean of 11.08 and standard deviation of 8.64. The standard deviation for the population of students who sit in the front is assumed to be the same as that for those who sit in the back. Test the claim at the 0.01 significance level.

a.	2.895	b.	13.281
c.	2.892	d.	10.933 please solve it all

Answer 1

Solution:-

1)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁< u₂
Alternative hypothesis: u₁ > u₂

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 2.13683
DF = 69

t = [ (x₁ - x₂) - d ] / SE

t = 2.89

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is thesize of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

The observed difference in sample means produced a t statistic of 2.89.

Therefore, the P-value in this analysis is 0.003.

Interpret results. Since the P-value (0.003) is less than the significance level (0.01), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that The average weekly number of hours spent studying by students who sit in the front of the classroom is greater than that of students who sit in the back of the classroom.