Is there a relationship between confidence intervals and two-tailed hypothesis tests? Letcbe the level of confidence used to construct a confidence interval from sample data. Letbe 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 significanceand null hypothesisH₀:=k,werejectH₀wheneverkfallsoutsidethec= 1confidence interval forbased on the sample data. Whenkfalls within thec= 1confidence interval, we do not rejectH₀.(A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such asp,₁₂, orp₁p₂, which we will study later.) Whenever the value ofkgiven in the null hypothesis fallsoutsidethec= 1confidence interval for the parameter, wereject H₀. For example, consider a two-tailed hypothesis test with= 0.01andH₀:= 20 H₁:20A random sample of size35has a sample meanx=23from a population with standard deviation=6.(a) What is the value ofc= 1? Construct a 1confidence interval forfrom the sample data. (Round your answers to two decimal places.)

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What is the value ofgiven in the null hypothesis (i.e., what isk)? k= Is this value in the confidence interval?

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Do we reject or fail to rejectH₀based on this information?

We fail to reject the null hypothesis since= 20 is not contained in this interval.We fail to reject the null hypothesis since= 20 is contained in this interval. We reject the null hypothesis since= 20 is not contained in this interval.We reject the null hypothesis since= 20 is contained in this interval.

(b) Using methods of this chapter, find theP-value for the hypothesis test. (Round your answer to four decimal places.)