Assume that the populations follow a normal distribution with equal variances. Is there a difference in the mean amount of time boys and girls spend playing sports each day? Test at 5% level of significance.
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- For any normal distribution, what is the probablity of selection a score less than the mean?Show that E[Sample Variance] = Population VarianceWe want to estimate the mean distance travelled to work by employees of a large manufacturing firm. Past studies indicate that the variance of these distances is 4.0 km2and that the distances follow a normal distribution. How many employees should be chosen at random and polled if the estimated mean distance is to be within 0.1 km ofthe true mean with a confidence level of 95%?
- If, in an analysis of variance, you find that MSTR is greater than MSE, why can you not immediately reject the null hypothesis without determining the F ratio and its distribution? Explain.13The distance of a single score from the mean - for example, the distance of your exam score from the average exam score for the entire class - is referred to as what? O Deviation O Variance Sum of Squared deviations (S.S.) Standard deviation
- A researcher wants to measure average cardiovascular health of university students and compare those scores to the average scores in the general population. Assuming that population variance is known, what statistical test is most appropriate for this study? independent-samples t-test single-sample t-test z-test for sample mean related-samples t-testMembers of fraternities and sororities are required to volunteer for community service. Do fraternity brothers work an equal number of volunteer hours on average compared to sorority sisters? The data below show the number of volunteer hours worked for twelve randomly selected fraternity brothers and thirteen randomly selected sorority sisters. Brothers: 12 12 12 14 10 Sisters: 8 6 7 2 5 4 Assume both follow a Normal distribution. What can be concluded at the a = 0.10 level of significance level of significance? For this study, we should use t-test for the difference between two independent population means Ho: H₁: μ1 μ1 b. The test statistic t a. The null and alternative hypotheses would be: c. The p-value = 0.0015 d. The p-value is ≤ ✓ = 2 a 4 12 5 3 4 13 7 5 7 7666 μ2 μ2 (please enter a decimal) (Please enter a decimal) 3.592 X (please show your answer to 3 decimal places.) X (Please show your answer to 4 decimal places.)When you take samples of size n - 100 from a normally distributed population, what will likely be the shape of the distribution of sample means? Right Skewed Left Skewed Normal