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Null and Alternative Hypothesis, Type I and II error, T test for equal variances

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Exercise I
The admissions counselors at Brainy University believe that the freshman class they have just recruited is the brightest yet. If they wanted to test this belief (that the freshman are brighter than the other classes, what would the null and alternative hypothesis be?

To test the hypothesis in Exercise 1, the admissions counselors select a random sample of freshmen and compare their scores on the SAT to those of the population of upperclassmen. They find that the freshmen do in fact have a higher mean SAT score. However, what they are unaware of is that the sample of freshmen was not representative of all freshmen at Brainy University. In fact, the sample overrepresented those with high scores and underrepresented those with low scores. What type of error (Type I or Type II) did the counselors make?

Exercise 2

What are the appropriate Ho and Ha for each of the following research studies? In addition, note whether the hypothesis test is one or two tailed.

a. A study in which researchers want to test whether there is a difference in spatial ability between left- and right-handed people
b. A study in which researchers want to test whether nurses who work 8-hour shifts deliver higher-quality work than those who work 12-hour shifts
c. A study in which researchers want to determine whether crate-training puppies is superior to training without a crate.

Exercise 3
A college student is interested in whether there is a difference between male and female students in the amount of time spent studying each week. The student gathers information from a random sample of male and female students on campus. Amount of time spent studying is normally distributed. The data follow.
Males
27, 25, 19, 10, 16, 22, 14
Females
25, 29, 18, 23, 20, 15, 19
a. What statistical test should be used to analyze these data?
b. Identify H0 and Ha for this study.
c. Conduct the appropriate analysis.
d. Should H0 be rejected? What should the researcher conclude? e. If significant, compute the effect size and interpret. f. If significant, draw a graph representing the data.

Exercise 4
What is the standard error of the difference between means

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Solution Summary

This solution is comprised of a detailed explanation for defining the null and alternative hypotheses and identifying the type I and type II error from the question. The solution also depicts how two sample t tests can be applied to data and all step-by-step calculations are shown. A detailed explanation is provided for all questions.

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