Use the sample results from the previous problem to test the claim that the generated values are from a population with a standard deviation equal to $12.5$. Use a $0.05$ significance level.

Use a significance level of $\alpha=0.05$. When eight bears were anesthetized, researchers measured the distances (in inches) around the bears' chests and weighed the bears (in pounds). Minitab was used to find that the value of the linear correlation coefficient is r=0.993. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?

Finish the following sentence.

Overall, the average level of performance in an industry is likely to be highest when ___________.

A) the threat level of all five forces is high

B) the threat level of rivalry and substitutes is low, but the threat level of suppliers, buyers and new entrants is high

C) the threat level of rivalry, substitutes and new entrants is high, but the threat level of buyers and supplies is low

D) the threat level of all five forces is low

Find the critical values of $r$ for a test of the claim that there is a linear correlation between two variables, given that the sample consists of 15 pairs of data and the significance level is $0.05$.

Use the Wilcoxon matched-pairs signed-ranks test to test the given hypotheses at the $\alpha$=0.05 level of significance. The dependent sample were obtained randomly. Hypotheses: $H_{0}: M_{D}=0$ versus $H_{1}: M_{D} \neq 0$ with n=14, $T_{-}=-45$, and $T_{+}=60$.

A study with 12 subjects reported a result that failed to achieve statistical significance at the 5% level. The P-value was 0.052. Write a short summary of how you would interpret these findings.

You would like to determine if the population probability of success differs from $0.70$. You find 62 successes in 80 binomial trials. Implement the test at the $1 \%$ level of significance.

For a given data set containing $26$ points, the assumptions of the linear model are satisfied. The following values are computed: $b_1 = 46.8$ and $s_b = 15.2$. Perform a test of the hypothesis $H_0 : \beta_1 = 0$ versus $H_1: \beta_1 > 0$. Use the $\alpha = 0.01$ level of significance. Can you conclude that the explanatory variable is useful in predicting the outcome variable? Explain.

Using the Standard Normal table, find the $z_{\alpha/2}$ value for a $95 \%$ confidence level.

A) $1.69$

B) $2.33$

C) $1.96$

D) $1.645$

Consider the following hypotheses:

$$\begin{aligned} & H_0: \mu=120 \\ & H_A: \mu \neq 120 \end{aligned}$$

The population is normally distributed with a population standard deviation of 46 .

a. Use a 5% level of significance to determine the critical value(s) of the test.

b. What is the conclusion with $\bar{x}=132$ and $n=50$ ?

c. Use a 10% level of significance to determine the critical value(s) of the test.

A random sample of 60 binomials trials resulted in 18 successes. Test the claim that the population proportion of successes exceeds 18%. Use a level of significance of 0.01 What do the results tell you?

Assume that the populations are normally distributed. Test whether $\mu_{1}>\mu_{2}$ at the $\alpha$=0.05 level of significance for the given sample data.

$$\begin{matrix} \text{ } & \text{Sample 1} & \text{Sample 2}\\ \text{n} & \text{23} & \text{13}\\ \text{}{ \bar{x}} & \text{43.1} & \text{41.0}\\ \text{s} & \text{4.5} & \text{5.1}\\ \end{matrix}$$

For a given data set containing $18$ points, the assumptions of the linear model are satisfied. The following values are computed: $b_1 = 5.58$ and $s_b = 4.42$. Perform a test of the hypothesis $H_0 : \beta_1 = 0$ versus $H_1: \beta_1 \ne 0$. Use the $\alpha = 0.05$ level of significance. Can you conclude that the explanatory variable is useful in predicting the outcome variable? Explain.

Use the Wilcoxon matched-pairs signed-ranks test to test the given hypotheses at the $\alpha$=0.05 level of significance. The dependent sample were obtained randomly. Hypotheses: $H_{0}: M_{D}=0$ versus $H_{1}: M_{D} \neq 0$ with n=18, $T_{-}=-121$, and $T_{+}=50$.