Purchase Solution

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

Not what you're looking for?

Ask Custom Question

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

Purchase this Solution
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.

Solution Preview

Hi Dear,
Please find the solution of your posting. I hope it will ...

Purchase this Solution
Free BrainMass Quizzes
Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

View More Free Quizzes
Related BrainMass Solutions

  • Hypothesis Testing

    Item 5: What do/may Type I and Type II errors have to do with the type of test you might conduct (upper or lower tail) or the selection of the level of significance? Type I error is also called an "error of the first kind" or an "α error".

  • T-Test, Effect Size, Power

    The power equals 1 - β, where β is the Type II error rate ("false negative" error, i.e. the alternative hypothesis is actually true, but you do not reject the null hypothesis). Here, 0.9979 = 1 - β, so β = 0.0021.

  • Multiple choice questions on Test of hypothesis

    181694 Multiple choice questions on Test of hypothesis 1) If a test of a hypothesis has a Type 1 error probability (a) of 0.01, we mean: A) if the null hypothesis is true, we don't reject it 1% of 0.01 of the time(B) if the null hypothesis is true

  • Testing of hypothesis - logical questions

    It is TRUE because type I error and type II errors are related. If you are increasing the one, the other will decrease.

  • Difference Between Type I and Type II Error in Statistics

    Here are your hypotheses: Null hypothesis: mean is equal to 100 Alternate hypothesis: mean is different from 100 Example of a type I error: If you did your statistical test and found a low p-value (p < 0.05), and rejected the null hypothesis

  • General Statistics Null Hypothesis

    For this situation, state the null and alternative hypotheses in verbal terms, then identify what would constitute a Type I error and a Type II error in this situation. 1 What is the difference between a null hypothesis and an alternative hypothesis?

  • MCQs: ANOVA

    * using several t test increases the risk of a Type II error In an analysis of variance, differences between participants contribute to which of the following variances?

  • Hypothesis Testing: Internet Usage for a Company

    Alternative hypothesis: The mean internet usage for a country in 2017 is not 60%. Ho: μ = 60 Ha: μ ≠ 60 A Type I error occurs if the null hypothesis is true but we reject it.

  • Blood Pressures: Null and Alternate Hypothesis and Type I Errors

    Based on this information, answer the questions below: What are the null hypothesis (Ho) and the alternative hypothesis (H1) that should be used for the test? Ho: μ is? H1: μ is? In the context of this test, what is a Type I error?

View More Related Solutions