# A researcher is interested in determining if there is a significant difference i

aortiH 2021-10-24 Answered
A researcher is interested in determining if there is a significant difference in number of hours of studying in a week between male and female undergraduate students. 15 randomly selected males and 15 randomly selected females from across all majors were used in the study. The mean for females was determined to be 10 hours with a standard deviation of 2.5 hours and the mean for males was determined to be 7.25 with a standard deviation of 2.25 hours. Using an alpha of .05 is there enough evidence that females study on average more than males??
a. Write the hypotheses for this scenario.
b. Is this one tailed or two tailed? Why?
c. What statistical test would be used for this scenario? Explain why.
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## Expert Answer

broliY
Answered 2021-10-25 Author has 97 answers

Part a
State the hypotheses.
Let ${\mu }_{1}$ be the mean hours studying in a week for females.
Let ${\mu }_{2}$ be the mean hours studying a week formales.
Null hypothesis: ${H}_{0}:{\mu }_{1}-{\mu }_{2}=0$
That is, there is no evidence to conclude that mean hours of studying for females on everage is more than males.
Alternative hypothesis: ${H}_{a}:{\mu }_{1}-{\mu }_{2}>0$
That is, there is evidence to conclude that mean hours of studying for females on average is more than males.
Part b
Determine the whether the test is one or two tailed.
From the information, given the claim to test is whether the mean hours of studying for females on average are more than males or not.
It is clear that the direction of the tail in the given problem is single tail and because the tail of the direction indicates right tail.
Therefore, the test is of clearly one tailed.
Part c
Identify the type of statistical test used here.
The type of test used here is two sample t test because it is is used to check if the averages of two groups are statistically different from each other or not.
Moreover, the significant difference between the two groups can be analyzed using t test when the sample size is small, population variances are unknown and the populations are normally distributed
Thus, the type of statistical test used here is two sample t test.
Step 4
Use EXCEL MEGASTAT to obtain the value of the test statistic and the P-value.
EXCEL MEGASTAT procedure:
Step 1: In EXCEL, Select Add-Ins>Mega Stat>Hypothesis Tests.
Step 2: Choose compare Two Independent Groups.
Step 3: Choose Summary input.
Step 4: In Group 1, enter B1:D4 (Select range with label teenager boys, mean 10, SD 2.5, n 15).
Step 5: In Group 2, enter D1:D4 (Select range with label teenager girls, mean 7.25, SD 2.25, n 15)
Step 6: Enter 0 Under Hypothesized difference.
Step 7: Check t-test, enter Confidence level as 95.2.
Step 8: Choose greater than in alternative.
Step 9: Click OK.
EXCEL MEGASTAT output:
Hypothesis Test: Independent Groups (t-test, unequal variance)
$\begin{array}{|cc|}\hline females& males\\ 10& 7.25& mean\\ 2.5& 2.25& std.dev.\\ 15& 15& n\\ \hline\end{array}$
27 df
2.75000 difference (females - males)
0.86843 standard error of difference
0 hypothesized difference
3.17 t
.0019 p-value (one-tailed, upper)
From the Excel MEGASTAT output, the test statistic is 3.17 and the p-value is 0.0019.
The conclusion is obtained as shown below:
Use the level of significance is 0.05.
The p-value is less of significance.
That is, p-value $\left(=0.0019\right)<\alpha \left(=0.05\right)$
By rejection rule, reject the null hypothesis.
That is, there evidence to conclude that mean hours of studying for females on average is more than males.

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