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

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 2021-01-27

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 2020-12-24

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?