Question

A recent study focused on the amount of money single men and women save monthly. The information is summarized next. Assume that the population standard deviations are equal. Sample Size Sample Mean Population Standard Deviation Men 25 23 5 Women 30 28 10 At the .01 significance level, do women save more money than men? What is the test statistic for this hypothesis? Select one: a. z-statistic b. t-statistic c. p-statistic d. df-statistic

Answer 1

The appropriate test statistic for determining if there is a significant difference in the monthly savings between single men and women, given that the population standard deviations are known and assumed equal, is the z-statistic.

Step-by-step explanation:

The question pertains to conducting a hypothesis test to determine if there is a significant difference in the amount of money saved by single men and women on a monthly basis. As the population standard deviations are assumed to be equal and known, the appropriate test statistic would be a z-statistic. With a sample size of 25 men and 30 women and at a .01 significance level, you would compare the z-statistic calculated from the sample data to a critical value from the z-distribution to determine if women save more than men.

Answer 2

Both means are apprxoimately equal at 1% level of significance.

Step-by-step explanation:

Given is the information summarised below

Group Men Women

Mean 23.00 28.00

SD 5.00 10.00

SEM 1.00 1.83

N 25 30

H0: Mean of mean = mean of women

Ha: means of men < mean of women

(Left tailed test)

Since population std deviation is known but sample sizes are small t test is used.

The mean of Men minus Women equals -5.00

standard error of difference = 2.201

t = 2.2721

df = 53

p value= 0.0136

since p >0.01 at 1% significance level we fail to reject H0.

Both means are apprxoimately equal at 1% level of significance.