The conclusion based on the two-tailed test is more conservative.

2021-03-06

asked 2020-12-24

In there a relationship between confidence intervals and two-tailed hypothesis tests? The
answer is yes. Let c be the level of confidence used to construct a confidence interval from sample data. Let * be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean:
For a two-tailed hypothesis test with level of significance a and null hypothesis H_0 : mu = k we reject Ho whenever k falls outside the c = 1 — alpha confidence interval for mu based on the sample data. When A falls within the c = 1 — alpha confidence interval. we do reject H_0.
For a one-tailed hypothesis test with level of significance Ho : mu = k and null hypothesiswe reject Ho whenever A falls outsidethe c = 1 — 2alpha confidence interval for p based on the sample data. When A falls within thec = 1 — 2alpha confidence interval, we do not reject H_0.
A corresponding relationship between confidence intervals and two-tailed hypothesis tests is also valid for other parameters, such as p,mu1 — mu_2, and p_1, - p_2.
(b) Consider the hypotheses H_0 : p_1 — p_2 = O and H_1 : p_1 — p_2 != Suppose a 98% confidence interval for p_1 — p_2 contains only positive numbers. Should you reject the null hypothesis when alpha = 0.05? Why or why not?

asked 2021-01-31

In there a relationship between confidence intervals and two-tailed hypothesis tests? The answer is yes. Let c be the level of confidence used to construct a confidence interval from sample data. Let * be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean:

For a two-tailed hypothesis test with level of significance a and null hypothesis \(H_{0} : \mu = k\) we reject Ho whenever k falls outside the \(c = 1 — \alpha\) confidence interval for \(\mu\) based on the sample data. When A falls within the \(c = 1 — \alpha\) confidence interval. we do reject \(H_{0}\).

For a one-tailed hypothesis test with level of significance Ho : \(\mu = k\) and null hypothesiswe reject Ho whenever A falls outsidethe \(c = 1 — 2\alpha\) confidence interval for p based on the sample data. When A falls within the \(c = 1 — 2\alpha\) confidence interval, we do not reject \(H_{0}\).

A corresponding relationship between confidence intervals and two-tailed hypothesis tests is also valid for other parameters, such as p, \(\mu1 — \mu_2,\ and\ p_{1}, - p_{2}\).

(a) Consider the hypotheses \(H_{0} : \mu_{1} — \mu_{2} = O\ and\ H_{1} : \mu_{1} — \mu_{2} \neq\) Suppose a 95% confidence interval for \(\mu_{1} — \mu_{2}\) contains only positive numbers. Should you reject the null hypothesis when \(\alpha = 0.05\)? Why or why not?

For a two-tailed hypothesis test with level of significance a and null hypothesis \(H_{0} : \mu = k\) we reject Ho whenever k falls outside the \(c = 1 — \alpha\) confidence interval for \(\mu\) based on the sample data. When A falls within the \(c = 1 — \alpha\) confidence interval. we do reject \(H_{0}\).

For a one-tailed hypothesis test with level of significance Ho : \(\mu = k\) and null hypothesiswe reject Ho whenever A falls outsidethe \(c = 1 — 2\alpha\) confidence interval for p based on the sample data. When A falls within the \(c = 1 — 2\alpha\) confidence interval, we do not reject \(H_{0}\).

A corresponding relationship between confidence intervals and two-tailed hypothesis tests is also valid for other parameters, such as p, \(\mu1 — \mu_2,\ and\ p_{1}, - p_{2}\).

(a) Consider the hypotheses \(H_{0} : \mu_{1} — \mu_{2} = O\ and\ H_{1} : \mu_{1} — \mu_{2} \neq\) Suppose a 95% confidence interval for \(\mu_{1} — \mu_{2}\) contains only positive numbers. Should you reject the null hypothesis when \(\alpha = 0.05\)? Why or why not?

asked 2020-12-30

For the same data, null hypothesis, and level of significance, is it possible that a one-tailed test results in the conclusion to reject Hg while a two tilled test results in the conclusion to fail to reject Ho? Explain.

asked 2020-12-24

For the same data, null hypothesis, and level of significance, if the conclusion is to reject \(H_{0}\) based on a two-tailed test, do you also reject Ho based on a one-tailed test? Explain.

asked 2021-06-22

A bank wants to know which of two incentive plans will most increase the use of its credit cards. It offers each incentive to a group of current credit card customers, determined at random, and compares the amount charged during the following six months. What type of study design is being used to produce data?

asked 2021-05-14

When σ is unknown and the sample size is \(\displaystyle{n}\geq{30}\), there are tow methods for computing confidence intervals for μμ. Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When \(\displaystyle{n}\geq{30}\), use the sample standard deviation s as an estimate for σσ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σσ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?

asked 2021-01-27

Critical Thinking: One-Tailed versus Two-Tailed Tests For the same data and null hypothesis, is the P-value of a one-tailed test (right or left) larger or smaller than that of a two-tailed test? Explain.

asked 2021-05-14

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.

\(\begin{array}{|c|c|}\hline 11.8 & 7.7 & 6.5 & 6 .8& 9.7 & 6.8 & 7.3 \\ \hline 7.9 & 9.7 & 8.7 & 8.1 & 8.5 & 6.3 & 7.0 \\ \hline 7.3 & 7.4 & 5.3 & 9.0 & 8.1 & 11.3 & 6.3 \\ \hline 7.2 & 7.7 & 7.8 & 11.6 & 10.7 & 7.0 \\ \hline \end{array}\)

a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. \([Hint.\ ?x_{j}=219.5.]\) (Round your answer to three decimal places.)

MPa

State which estimator you used.

\(x\)

\(p?\)

\(\frac{s}{x}\)

\(s\)

\(\tilde{\chi}\)

b) Calculate a point estimate of the strength value that separates the weakest \(50\%\) of all such beams from the strongest \(50\%\).

MPa

State which estimator you used.

\(s\)

\(x\)

\(p?\)

\(\tilde{\chi}\)

\(\frac{s}{x}\)

c) Calculate a point estimate of the population standard deviation ?. \([Hint:\ ?x_{i}2 = 1859.53.]\) (Round your answer to three decimal places.)

MPa

Interpret this point estimate.

This estimate describes the linearity of the data.

This estimate describes the bias of the data.

This estimate describes the spread of the data.

This estimate describes the center of the data.

Which estimator did you use?

\(\tilde{\chi}\)

\(x\)

\(s\)

\(\frac{s}{x}\)

\(p?\)

d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)

e) Calculate a point estimate of the population coefficient of variation \(\frac{?}{?}\). (Round your answer to four decimal places.)

State which estimator you used.

\(p?\)

\(\tilde{\chi}\)

\(s\)

\(\frac{s}{x}\)

\(x\)

\(\begin{array}{|c|c|}\hline 11.8 & 7.7 & 6.5 & 6 .8& 9.7 & 6.8 & 7.3 \\ \hline 7.9 & 9.7 & 8.7 & 8.1 & 8.5 & 6.3 & 7.0 \\ \hline 7.3 & 7.4 & 5.3 & 9.0 & 8.1 & 11.3 & 6.3 \\ \hline 7.2 & 7.7 & 7.8 & 11.6 & 10.7 & 7.0 \\ \hline \end{array}\)

a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. \([Hint.\ ?x_{j}=219.5.]\) (Round your answer to three decimal places.)

MPa

State which estimator you used.

\(x\)

\(p?\)

\(\frac{s}{x}\)

\(s\)

\(\tilde{\chi}\)

b) Calculate a point estimate of the strength value that separates the weakest \(50\%\) of all such beams from the strongest \(50\%\).

MPa

State which estimator you used.

\(s\)

\(x\)

\(p?\)

\(\tilde{\chi}\)

\(\frac{s}{x}\)

c) Calculate a point estimate of the population standard deviation ?. \([Hint:\ ?x_{i}2 = 1859.53.]\) (Round your answer to three decimal places.)

MPa

Interpret this point estimate.

This estimate describes the linearity of the data.

This estimate describes the bias of the data.

This estimate describes the spread of the data.

This estimate describes the center of the data.

Which estimator did you use?

\(\tilde{\chi}\)

\(x\)

\(s\)

\(\frac{s}{x}\)

\(p?\)

d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)

e) Calculate a point estimate of the population coefficient of variation \(\frac{?}{?}\). (Round your answer to four decimal places.)

State which estimator you used.

\(p?\)

\(\tilde{\chi}\)

\(s\)

\(\frac{s}{x}\)

\(x\)

asked 2021-05-05

If John, Trey, and Miles want to know how’ |
many two-letter secret codes there are that don't
have a repeated letter. For example, they want to
: count BA and AB, but they don't want to count“ doubles such as ZZ or XX. Jobn says there are
26 + 25 because you don’t want to use the same
letter twice; that’s why the second number is 25.

‘Trey says he thinks it should be times, not plus: 26-25, Miles says the number is 26-26 ~ 26 because you need to take away the double letters. Discuss the boys’ ideas, Which answers are correct, which are not, and why? Explain your answers clearly and thoroughly, drawing ‘on this section’s definition of multiptication.. -

‘Trey says he thinks it should be times, not plus: 26-25, Miles says the number is 26-26 ~ 26 because you need to take away the double letters. Discuss the boys’ ideas, Which answers are correct, which are not, and why? Explain your answers clearly and thoroughly, drawing ‘on this section’s definition of multiptication.. -

asked 2021-06-01

(a) What is the value of c\(\displaystyle{c}={1}-\alpha\);. Using the methods, construct a \(\displaystyle{c}={1}-\alpha\); confidence interval for μ from the sample data. What is the value of \(\mu\); given in the null hypothesis (i.e., what is k)? Is this value in the confidence interval? Do we reject or fail to reject \(H_0\) based on this information?

(b) using methods, find the P-value for the hypothesis test. Do we reject or fail to reject \(H_0\)? Compare your result to that of part (a).