A. Look for the definitions of the following terms related to hypothesis testing.

1. Null Hypothesis

2. Level of Significance

3. Type I error

1. Null Hypothesis

2. Level of Significance

3. Type I error

texelaare
2020-12-28
Answered

1. Null Hypothesis

2. Level of Significance

3. Type I error

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asked 2022-06-25

A company produces millions of 1-pound packages of bacon every week. Company specifications allow for no more than 3 percent of the 1-pound packages to be underweight. To investigate compliance with the specifications, the company’s quality control manager selected a random sample of 1,000 packages produced in one week and found 40 packages, or 4 percent, to be underweight.

Assuming all conditions for inference are met, do the data provide convincing statistical evidence at the significance level of $\alpha =0.05$ that more than 3 percent of all the packages produced in one week are underweight?

(A) Yes, because the sample estimate of 0.04 is greater than the company specification of 0.03.

(B) Yes, because the p-value of 0.032 is less than the significance level of 0.05.

(C) Yes, because the p-value of 0.064 is greater than the significance level of 0.05.

(D) No, because the p-value of 0.032 is less than the significance level of 0.05.

(E) No, because the p-value of 0.064 is greater than the significance level of 0.05.

The answer is (B) and I was trying to understand why. My calculation was:

${H}_{a}:p>0.03$

$z=\frac{\hat{p}-{p}_{0}}{\sqrt{\frac{{p}_{0}(1-{p}_{0})}{n}}}$

$z=\frac{0.04-0.03}{\sqrt{\frac{(0.03)(0.07)}{1000}}}$

But I get a ridiculously high number. I'm confused about how to get the p-value in this case.

A two-sided t-test for a population mean is conducted of the null hypothesis ${H}_{0}:\mu =100$. If a 90 percent t-interval constructed from the same sample data contains the value of 100, which of the following can be concluded about the test at a significance level of $\alpha =0.10$?

(A) The p-value is less than 0.10, and ${H}_{0}$ should be rejected.

(B) The p-value is less than 0.10, and ${H}_{0}$ should not be rejected.

(C) The p-value is greater than 0.10, and ${H}_{0}$ should be rejected.

(D) The p-value is greater than 0.10, and ${H}_{0}$ should not be rejected.

(E) There is not enough information given to make a conclusion about the p-value and ${H}_{0}$.

Here the answer is D, but again I am confused. How can I find the p-value in this case?

Assuming all conditions for inference are met, do the data provide convincing statistical evidence at the significance level of $\alpha =0.05$ that more than 3 percent of all the packages produced in one week are underweight?

(A) Yes, because the sample estimate of 0.04 is greater than the company specification of 0.03.

(B) Yes, because the p-value of 0.032 is less than the significance level of 0.05.

(C) Yes, because the p-value of 0.064 is greater than the significance level of 0.05.

(D) No, because the p-value of 0.032 is less than the significance level of 0.05.

(E) No, because the p-value of 0.064 is greater than the significance level of 0.05.

The answer is (B) and I was trying to understand why. My calculation was:

${H}_{a}:p>0.03$

$z=\frac{\hat{p}-{p}_{0}}{\sqrt{\frac{{p}_{0}(1-{p}_{0})}{n}}}$

$z=\frac{0.04-0.03}{\sqrt{\frac{(0.03)(0.07)}{1000}}}$

But I get a ridiculously high number. I'm confused about how to get the p-value in this case.

A two-sided t-test for a population mean is conducted of the null hypothesis ${H}_{0}:\mu =100$. If a 90 percent t-interval constructed from the same sample data contains the value of 100, which of the following can be concluded about the test at a significance level of $\alpha =0.10$?

(A) The p-value is less than 0.10, and ${H}_{0}$ should be rejected.

(B) The p-value is less than 0.10, and ${H}_{0}$ should not be rejected.

(C) The p-value is greater than 0.10, and ${H}_{0}$ should be rejected.

(D) The p-value is greater than 0.10, and ${H}_{0}$ should not be rejected.

(E) There is not enough information given to make a conclusion about the p-value and ${H}_{0}$.

Here the answer is D, but again I am confused. How can I find the p-value in this case?

asked 2021-01-24

What is the decision at a 0.05 level of significance for each of the following tests?

F(3, 26) = 3.00

Retain or reject the null hypothesis?

F(4, 55) = 2.54

Retain or reject the null hypothesis?

F(4, 30) = 2.72

Retain or reject the null hypothesis?

F(2, 12) = 3.81

Retain or reject the null hypothesis?

F(3, 26) = 3.00

Retain or reject the null hypothesis?

F(4, 55) = 2.54

Retain or reject the null hypothesis?

F(4, 30) = 2.72

Retain or reject the null hypothesis?

F(2, 12) = 3.81

Retain or reject the null hypothesis?

asked 2021-05-28

Find the margin of error for the given values of c,s, and n. c=0.95, s=2.2, n=64

asked 2022-07-01

How will you formulate the appropriate null and alternativehypotheses on a population mean.

asked 2022-07-10

Life Expectancies Is there a relationship between the life expectancy for men and the life expectancy for women in a given country? A random sample of nonindustrialized countries was selected, and the life expectancy in years is listed for both men and women. Are the variables linearly related?

$\begin{array}{|ccccccc|}\hline \text{Men}& 56.8& 53.6& 70.6& 61.5& 44.6& 51.7\\ \text{Women}& 64.4& 46.2& 72.2& 20.2& 48.4& 47.1\\ \hline\end{array}$

(a) Compute the value of the correlation coefficient. Round your answer to at least three decimal places.

r=

(b) Stat the hypotheses.

${H}_{0}\phantom{\rule{0ex}{0ex}}{H}_{1}$

(c) Test the significance of the correlation coefficient at a=0.01 and 0.10 using The Critical Values for the PPMC Table.

Critical value(s): $\pm $

Reject/do not reject the null hypothesis

(d) Give a brief explanation of the type of relationship.

There is/is not (Choose one) a significant

(a) Compute the value of the correlation coefficient. Round your answer to at least three decimal places.

r=

(b) Stat the hypotheses.

${H}_{0}\phantom{\rule{0ex}{0ex}}{H}_{1}$

(c) Test the significance of the correlation coefficient at a=0.01 and 0.10 using The Critical Values for the PPMC Table.

Critical value(s): $\pm $

Reject/do not reject the null hypothesis

(d) Give a brief explanation of the type of relationship.

There is/is not (Choose one) a significant

$\begin{array}{|ccccccc|}\hline \text{Men}& 56.8& 53.6& 70.6& 61.5& 44.6& 51.7\\ \text{Women}& 64.4& 46.2& 72.2& 20.2& 48.4& 47.1\\ \hline\end{array}$

(a) Compute the value of the correlation coefficient. Round your answer to at least three decimal places.

r=

(b) Stat the hypotheses.

${H}_{0}\phantom{\rule{0ex}{0ex}}{H}_{1}$

(c) Test the significance of the correlation coefficient at a=0.01 and 0.10 using The Critical Values for the PPMC Table.

Critical value(s): $\pm $

Reject/do not reject the null hypothesis

(d) Give a brief explanation of the type of relationship.

There is/is not (Choose one) a significant

(a) Compute the value of the correlation coefficient. Round your answer to at least three decimal places.

r=

(b) Stat the hypotheses.

${H}_{0}\phantom{\rule{0ex}{0ex}}{H}_{1}$

(c) Test the significance of the correlation coefficient at a=0.01 and 0.10 using The Critical Values for the PPMC Table.

Critical value(s): $\pm $

Reject/do not reject the null hypothesis

(d) Give a brief explanation of the type of relationship.

There is/is not (Choose one) a significant

asked 2022-06-15

The log return X on a certain stock investment is an N(μ,σ2) random variable.

A financial analyst has claimed that the volatility σ of the log return on this stock is less than 3 units. A random sample of 11 returns on this stock gave an estimated variance of the log-returns as s2=16.

Assess the analyst's claim by using a significance test at level

α=0.05 to test

H0:σ2≤9 against H1:σ2>9.

Find a two-sided 95% confidence interval for σ2.

A financial analyst has claimed that the volatility σ of the log return on this stock is less than 3 units. A random sample of 11 returns on this stock gave an estimated variance of the log-returns as s2=16.

Assess the analyst's claim by using a significance test at level

α=0.05 to test

H0:σ2≤9 against H1:σ2>9.

Find a two-sided 95% confidence interval for σ2.

asked 2022-04-02

Explain why it is necessary to examine the residuals.