A researcher has reason to believe that the average sediment size of a particula

Question

A researcher has reason to believe that the average sediment size of a particular river is larger than the average sediment size of the watershed in which the river is contained. Previous research shows that the average size of sediment throughout the watershed containing the river is 0.54 mm. She measures 44 samples from her study site and finds the average sediment size to be 0.60 mm with a standard deviation of 0.12 mm. Can we be 99% confident that the mean of the sediment size for the river is greater than the mean of the sediment size for the entire watershed?

(All calculations should be carried to 4 decimal places. Report answers to two decimal places.) What is the critical value? What is the value of the test statistic? What decision is made regarding the null hypothesis?

(Do you “reject” or “fail to reject” the null hypothesis?)

Explanation / Answer

here for 99% CI, critcal value =2.3263

here std error =std deviation/(n)1/2 =0.0181

also test stat z=(X-mean)/std error =(0.6-0.54)/0.0181=3.3166

as test stat is higher then critical value and lies in rejection region we reject null hypothesis.

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