Exercises:Section 1

1. A sample of n=30 bags of Nestl's Raisinets were analyzed in August of 2012 by a Baruch class.The net weights in grams of the 30 bags are given, below.The data can be readily copied into Excel.

Below, a photo of a bag of Raisinets is shown with the stated net weight visible.Using that net weight (in grams) as the null hypothesis, conduct a t-test of that claim as follows.Begin with finding the sample average and sample standard deviation for the net weights of the sample of 30 bags of Raisinets.The alpha level of 5% is built-into your t-critical value table.That table is on page 3 of LN6.

(a) State the null and alternate hypotheses, both in words and in symbols.In those statements, reference the subject matter of this test.That is, refer not just to a generic population average, but specify what population is under study.

(b) Compute the raw distance between the sample average and the value of claimed by the null.

(c) With respect to the distance betweenand _o, under what conditions do we reject the null?

(d) Compute the standard error of the average.Show your work.

(e) Why are we going to divide the raw distance by the standard error of the average?

(f) Compute the t-statistic.Show your work.

(g) Find the degrees of freedom.

(h) Find the t-critical value (make sure you can its from the t-table.)

(i) State the rejection rule and then use it to decide whether or not the null hypothesis is rejected.

(j) Sketch the relevant t-distribution, showing with the location of the t-critical values and of zero.Show and label the rejection and non-rejection regions.Finally, show the location of your t-statistic.

Net Weights of Bags of Raisinets

46.9

46.9

47.1

47.1

46.2

43.4

45.7

43.8

46.2

45.6

45.3

47.3

45.1

46.2

47.2

48.9

45.9

45.2

46.5

46.5

47.0

47.9

46.7

46.4

48.0

46.5

44.3

45.9

46.8

47.1