Question

How does confidence internals confirm hypothesis testing results. Provide an example

Answer 1

interpretation:-

if for a test,

p value < level of significance()% , then we reject the null hypothesis.

if the (1-)% confidence interval does not contain the value of null hypothesis then we conclude that the null hypothesis gets rejected.

PROBLEM:-

a researcher claims that the mean time taken to cross a bridge is 2.6 minutes.Ram  randomly selected 14 people and found that the average time taken by them is 2.4 minutes and sample standard deviation is 0.9 minutes.is there sufficient evidence to support the researcher's claim?( use =0.05)

solution:-

hypothesis:-

given data:

sample size (n) = 14

sample sd (s) = 0.9

sample mean() = 2.4

hypothesized mean(M) = 2.6

test statistic be:-

df= (14-1 ) = 13

p value =0.421 ( using p value calculator , for df=13 ,t=-0.83, two sided test)

decision based on p value:-

p value=0.421 >0.05

so we fail to reject the null hypothesis .we conclude that there is enough evidence to support the researcher's claim.

decision based on confidence interval:-

95 % confidence interval = (1.881,2.919)

our confidence interval contains the null hypothesis value, i.e 2.6.

so, we fail to reject the null hypothesis .we conclude that there is enough evidence to support the researcher's claim.

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