The mean SAT score for 13 male high school students is 500 and the standard deviation is 100. The mean SAT score for 16 female high school students is 490 and the standard deviation is 80. At o=.05 sigma sign are male SAT scores more varied than female? (Sigma=.05)
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability of the Z score in relation to .05.
To determine whether the male SAT scores are more varied than the female SAT scores, we need to conduct a hypothesis test using the given information.
Step 1: Set up the hypotheses.
- Null hypothesis (H0): The standard deviation of male SAT scores is equal to or less than the standard deviation of female SAT scores.
- Alternative hypothesis (Ha): The standard deviation of male SAT scores is greater than the standard deviation of female SAT scores.
Step 2: Select the significance level.
In this case, the significance level (alpha) is given as 0.05.
Step 3: Compute the test statistic.
We can use the F-test to compare the variances of two independent samples, which is calculated as the ratio of the variances.
F = (S1^2 / S2^2)
where S1 is the sample standard deviation of the first group (male SAT scores) and S2 is the sample standard deviation of the second group (female SAT scores).
Step 4: Determine the rejection region.
Since the alternative hypothesis is stating that the standard deviation of male SAT scores is greater, we have a right-tailed test. We need to compare the computed F-value to the critical value from the F-distribution.
Step 5: Calculate the p-value.
The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true.
Step 6: Make a decision.
If the p-value is less than the significance level, we reject the null hypothesis and conclude that the male SAT scores are more varied than the female SAT scores. Otherwise, we fail to reject the null hypothesis.
Given that the sample sizes are small (n1 = 13, n2 = 16), we can rely on statistical software or a calculator to perform the calculations for the F-test and determine the p-value.