Statistics Project---Difference in Means We want to compare the mean GPA for fem

Question

Statistics Project---Difference in Means

We want to compare the mean GPA for females and males at Valencia. This project will ask you to take a random sample from the population of female GPAs and a random sample from the population of male GPAs. Use the Student Data I provided (same data as for the last project). The female GPAs are ID numbers 1 to 4573 and the male GPAs are ID numbers 4574 to 7903. Each person should generate their own random samples from these two groups. Show the random IDs and their corresponding GPAs.

1-What do the symbols ?1 and ?2 represent in the context of this problem? Be specific.

     U1 represent the mean GPA for all West Campus female students who have completed at least 30 credit hours. U2 represent the mean GPA for all West Campus male students who have completed at least 30 hours.

2-Take a random sample of twenty GPAs from each population (20 females and 20 males). Show the random IDs as well as the GPAs.

TABLE

3-Make a side by side box plot for the two sets of data (using StatCrunch or NEATLY drawn by hand with a very clearly labeled and accurate scale).

a)

b)Calculate the mean and standard deviation for each sample.

?1(Female mean) =2.8385 Standard Deviation Female= .7910770473

?2(Male mean) =2.7735     Standard Deviation Male= .6588049388

c)Does it appear that the assumptions needed to use the t-distribution are met?

Yes, The Assumptions needed does appear to use the t- distribution are met

3-Perform a hypothesis test at the 10% significance level to decide if there is a difference in the population means.

Sample for female:

Sample size =n1=20

Sample mean GPA = 2.8385

Sample standard Deviation=.7910770473

Sample for males:

Sample size=n2=20

Sample mean GPA =2.7735

Sample Standard Deviation=.658804388

a)State the hypotheses in symbols and write a sentence for the null hypothesis.

Ho=U1-U2=0

                Ha=U1-U2 ?0

           Null Hypothesis: There is no difference in mean GPA between females and    males

           Alternate hypothesis: there is significant differences in mean GPA between females and males

b)Sketch the sampling distribution, with the appropriate area shaded.

c)Calculate the P-value and, state your conclusion in context of GPAs.

using the calculator TI-84 under the t-distribution to the left of (.282365) and for (df=36.79517) is given by.3896229676

since the hypothesis, this is a two-tailed test. Hence, p-value = 2*.3896229676=.7792459352

p-value=.779245 , significant level .10

conclusion:

There is sufficient evidence to conclude that there is a significant difference in mean GPA between females and males

4-Construct a 90% confidence interval for the difference in population means.

a)Interpret your interval in terms of mean GPAs.

We are 90% confident that the difference in population mean is lies between -0.333 and 0.463      

Here population difference = 0 which lies in the confidence interval.

That is we accept the null hypothesis.

b)Does your interval allow you to conclude which population mean is higher?

No out interval does not allow to conclude which population mean is higher as it ranges from negative value to positive value.

c)If so, which one is higher and by how much?

N/A

5.Based on the confidence interval you calculated for question #4:

a-Is there a difference in the population means?

b-How can you tell from the confidence interval?

c-Does this agree with your conclusion in question #3?

Hi I just need the question # 5 answer a through c. thanks in advance

Explanation / Answer

5)
a) we can say that there is not a difference in the population means
b)
bacause 0 is present in 90 % confidence interval
c)

in Q3 , p-value = 0.779 > 0.10
hence we fail to reject the null hypothesis
and we conclude that there is not sufficient evidence to conclude that there
is significant difference in mean .
(Note your conclusion in Q3 is wrong)

hence this agrees with conclusion in Q3

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