Solution Found!
Answer: For the following exercises where applicable:a.
Chapter 8, Problem 19CQ(choose chapter or problem)
For the following exercises where applicable:
a. State the hypotheses and identity the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Use the traditional method of hypothesis testing unless otherwise specified. Assume all variables are normally distributed.
In a New York modeling agency, a researcher wishes to see if the average height of female models is really less than 67 inches, as the chief claims. A random sample of 20 models has an average height of 65.8 inches. The standard deviation of the sample is 1.7 inches. At \(\alpha=0.05\), is the average height of the models really less than 67 inches? Use the P-value method.
Questions & Answers
QUESTION:
For the following exercises where applicable:
a. State the hypotheses and identity the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Use the traditional method of hypothesis testing unless otherwise specified. Assume all variables are normally distributed.
In a New York modeling agency, a researcher wishes to see if the average height of female models is really less than 67 inches, as the chief claims. A random sample of 20 models has an average height of 65.8 inches. The standard deviation of the sample is 1.7 inches. At \(\alpha=0.05\), is the average height of the models really less than 67 inches? Use the P-value method.
ANSWER:Step 1 of 5
Given, the average height of female models is really less than 67 inches.
n = 20 and the sample standard deviation s = 1.7.
a). We need to state the hypotheses.
Null hypothesis :
The hypothesis is that sample observations result purely from chance.
We denoted denoted by \(H_{0}\).
Alternative hypothesis :
The alternative hypothesis we denoted by \(H_1,\ H_a\), is the hypothesis that sample observations are influenced by some non-random cause.
The null and alternative hypotheses:
\(\begin{array}{l} H_{0}=\mu=67 \\ H_{a}: \mu \neq 67 \text { (claim) } \end{array}\)
b). We need to find the critical value.
Given a sample of 20.
So n = 20.
The critical values are obtained from the t-distribution table at (n - 1) = (20 - 1) = 19 degrees of freedom.