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 cons

Question

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 cons

Elleanor Mckenzie 2021-01-31 Answered

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} : μ = k

we reject Ho whenever k falls outside the

c = 1 — α

confidence interval for

μ

based on the sample data. When A falls within the

c = 1 — α

confidence interval. we do reject

H_{0}

.
For a one-tailed hypothesis test with level of significance Ho :

μ = k

and null hypothesiswe reject Ho whenever A falls outsidethe

c = 1 — 2 α

confidence interval for p based on the sample data. When A falls within the

c = 1 — 2 α

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,

μ 1 — μ_{2}, a n d p_{1}, - p_{2}

.
(a) Consider the hypotheses

H_{0} : μ_{1} — μ_{2} = O a n d H_{1} : μ_{1} — μ_{2} \neq

Suppose a 95% confidence interval for

μ_{1} — μ_{2}

contains only positive numbers. Should you reject the null hypothesis when

α = 0.05

? Why or why not?

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d2saint0

Answered 2021-02-01 Author has 89 answers

The level of significance,

α = 0.05

The null hypothesis:

H_{0} : μ_{1} - μ_{2} = 0

The alternative hypothesis:

H_{0} : μ_{1} - μ_{2} \neq 0

Here, from above hypothesis D = 0 and we know that for a two-tailed hypothesis test with level of significance

α

, we reject

H_{0}

whenever D falls outside the

c = 1 - α

confidence interval for

μ

based on the sample data. If a 95% confidence interval for

μ_{1} — μ_{2}

contains only positive numbers then we have to reject

H_{0}

at the level of significance

α = 0.05

.
Since, the confidence interval does not contain D = 0 and hence it falls outside the 95% confidence interval.

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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 cons

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