Question

Mean: 0.273 Median: 0.266. Sample Size: 30

Standard Deviation: 0.019 IQR: 0.022

Hypothesis is:  µ= 0.256 µ> 0.256

α=0.05

-State the conclusion to the hypothesis test, including the p-value for the test and a proper conclusion (reject the null hypothesis or fail to reject the null hypothesis) and what we then conclude about the population mean.

Report the confidence interval you calculated.

          i. Make sure you state it is a confidence interval for mean.

            ii. Give the proper interpretation of the confidence interval.

Answer 1

The null and alternative hypothesis is ,

The test is one-tailed test.

Since , the population standard deviation is unknown.

Therefore , use t-distribution.

Now , df=degreed of freedom=n-1=30-1=29

The test statistic is ,

The p-value is ,

p-value= ; The Excel function is , =TDIST(4.9007,29,1)

Decision : Here , p-value < 0.05

Therefore , reject the null hypothesis

The 95% confidence interval is ,

; ; The Excel function is , =TINV(0.05,29)

Here , the value 0.256 does not lies in the rejection region.

Therefore , reject the null hypothesis.