A study was conducted to investigate relationships between different types of standard test scores. On the Graduate Record Examination verbal test, 18 women had a mean of 538.82 and a standard
deviation of 114.16, and 12 men had a mean of 525.23 and a standard deviation of 97.23. Assume
that the two groups come from populations with the same standard deviation. Test the claim that the
mean score of women is equal to a mean score of men using a 0.02 significance level.
a) Define variables and extrapolate information from the word problem.
b) Claim:
c) Null Hypothesis, Ho:
Alternative Hypothesis, H1:
d) Graph of distribution (labeled) identifying the appropriate number of degrees of freedom (if
applicable), including critical regions, and significance level:
e) Critical Values:
f) Value of Test Statistic for sample:
g) Statistical Conclusion:
h) Sentence/Headline/Non-technical Conclusion in WORDS:
Can someone help me answer this? I am really stuck and in over my head with this, pleeeeeease help me...
You can probably use an independent groups t-test for this data.
Ho: µ1 = µ2
H1: µ1 does not equal µ2
Group 1 (Women)
mean = 538.82
standard deviation = 114.16
sample size = 18
Group 2 (Men)
mean = 525.23
standard deviation = 97.23
sample size = 12
degrees of freedom = n1 + n2 - 2 = 18 + 12 - 2 = 28
Use the appropriate statistical formula for this type of test. Calculate the test statistic using the information above. Find your critical value(s) using a t-distribution table at 0.02 level of significance for a two-tailed test with 28 degrees of freedom. Compare your test statistic to the critical value(s) from the table. If the test statistic exceeds either the positive or negative critical value from the table, reject the null and conclude a difference between the two populations. If the test statistic does not exceed the critical value, do not reject the null and conclude no difference between the two populations.
I hope this will help get you started.
a) In this problem, we are comparing the mean scores of women and men on a specific test. We are given the mean, standard deviation, and sample sizes for both groups.
b) The claim is that the mean score of women is equal to the mean score of men.
c) Null Hypothesis, Ho: The mean score of women is equal to the mean score of men.
Alternative Hypothesis, H1: The mean score of women is not equal to the mean score of men.
d) Since we are comparing means of two independent groups and assuming equal standard deviations, we can use a two-sample t-test. The distribution would be a t-distribution. We need to determine the degrees of freedom and identify the critical regions based on the significance level of 0.02. However, the degrees of freedom cannot be determined based on the given information.
e) To find the critical values, we need the degrees of freedom, which are not provided in the problem. Without this information, we cannot determine the critical values.
f) The test statistic value for the sample cannot be calculated without the degrees of freedom.
g) Without the critical values and test statistic, we cannot make a statistical conclusion.
h) We cannot draw a definitive conclusion without the necessary information.
It appears that the problem is incomplete or some information is missing. To solve it, we would need the degrees of freedom and the critical values based on the significance level.