### Statistical Hypothesis Testing ExampleA researcher claims that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B. The stomach contents of a sample of 14 blue crabs from Location A contain a mean of 194 milligrams of fish and a standard deviation of 37 milligrams. The stomach contents of a sample of 8 blue crabs from Location B contain a mean of 184 milligrams of fish and a standard deviation of 44 milligrams. At $\alpha = 0.05$, can you support the researcher's claim? Assume the population variances are equal. Complete parts (a) through (d) below.**(a) Identify the null and alternative hypotheses. Choose the correct answer below.**- A. $ H_0: \mu_1 - \mu_2 < 0 $ $ H_a: \mu_1 - \mu_2 = 0 $- B. $ H_0: \mu_1 - \mu_2 \leq 0 $ $ H_a: \mu_1 - \mu_2 > 0 $- C. $ H_0: \mu_1 - \mu_2 \geq 0 $ $ H_a: \mu_1 - \mu_2 < 0 $- D. $ H_0: \mu_1 - \mu_2 = 0 $ $ H_a: \mu_1 - \mu_2 \neq 0 $**(b) Find the standardized test statistic for $ \mu_1 - \mu_2 $**\[t = \_\_\_ \\text{(Round to three decimal places as needed.)}\]**(c) Calculate the P-value.**\[P = \_\_\_ \\text{(Round to four decimal places as needed.)}\]**(d) State the conclusion.**\[H_0 \: \text{There} \: \_\_\_\_\_\_ \: \text{enough evidence at the 5% level of significance to support the researcher's claim.}\]### ExplanationThe task involves determining whether there is statistical evidence to support the researcher's claim at a 5% significance level. 1. **Hypoth

For Location A:sample size (n1) = 14sample mean (x̄1) = 194sample standard deviation (s1) = 37For…

Answered: researcher claims that the stomachs of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The average height of students at a university from an SRS of 14 students gave a standard deviation of 2.5 feet. Construct a 95% confidence interval for the standard deviation of the height of students at the university. Assume normality for the data.
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A researcher decides to measure anxiety in group of bullies and a group of bystanders using a 23-item, 3 point anxiety scale. Assume scores on the anxiety scales are normally distributed and the variance among the group of bullies and bystanders are the same. A group of 30 bullies scores an average of 21.5 with a sample standard deviation of 10 on the anxiety scale. A group of 27 bystanders scored an average of 25.8 with a sample standard deviation of 8 on the anxiety scale. You do not have any presupposed assumptions whether bullies or bystanders will be more anxious so you formulate the null and alternative hypothesis based on that.
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