A recent study focused on the amount of money single men and women save monthly.
ID: 2934347 • Letter: A
Question
A recent study focused on the amount of money single men and women save monthly. The information is summarized here. Assume that the population standard deviations are equal.
At the 0.01 significance level, do women save more money than men? What is the critical value for this hypothesis test?
B)At the 0.01 significance level, do women save more money than men? What is the value of the test statistic for this hypothesis test?
Sample Size Sample Mean Population Standard Deviation Men 25 23 5 Women 30 28 10Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1< 2
Alternative hypothesis: 1 > 2
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. 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).
a)
tcritical = - 2.672
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 2.082
DF = 25 + 30 - 2
D.F = 53
b) t = [ (x1 - x2) - d ] / SE
t = - 2.40
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size 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 - 2.40. We use the t Distribution Calculator to find P(t < - 2.40) = 0.0099
Therefore, the P-value in this analysis is 0.0099
Interpret results. Since the P-value (0.0099) 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 women save more money than men.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.