NEED PART II

Comprehensive Task

The "Jupiter Bar" is a candy bar that is only manufactured and sold in one size. Tens of thousands of bars are manufactured every day. Nutritional content appears on the bar's wrapper, including a statement that a given bar has a sodium content of 96 milligrams.

Due to variability inherent in all manufacturing, we know that some bars would have slightly less than 96 milligrams of sodium and some bars would have more than 96 milligrams of sodium even if the value of "96 milligrams" appears on the wrapper. However, there is a concern that the average sodium content in all Jupiter Bars is actually more than 96 milligrams, and we have been asked to investigate.

Here are the sodium measurements (in milligrams) from a sample of 20 Jupiter Bars:

Sample mean=100.55

Sample standard deviation=6.34

Q1=97; median=101; Q3=104

Summary statistics n=20

Min = 88, max = 112

                  Dotplot                                                                       Boxplot

Part I

1) In the space above (labeledBoxplot, previous page), draw a boxplot for this dataset. Label Q1, the median, and Q3 on the boxplot.

2) In order for us to use this sample of n = 20 Jupiter Bars to make inferences about the whole population of Jupiter Bars, what assumption must we make regarding the sample and how it was obtained? What risk do we run in performing any inference about the population if this assumption is not met?

3) Assuming that the sampling was done properly, name two ways in which the summary information and graphs above suggest that the population average sodium content might be more than 96 milligrams? Hint: one thing to think about is the claim for the mean sodium content is and compare it to the mean found from the data in the table. Also look at dotplot to the left of the boxplot – does the data look symmetrical? What can you conclude from that?

Part II

Based on our analysis of our sample data, we are asked to perform a formal hypothesis test (test of significance) to examine if the average sodium content of all Jupiter Bars may actually be more than 96 milligrams.

1) Develop the correct null and alternative hypotheses using standard statistics symbols, using words, or using both.

2) Based on the context of the question we are investigating and the nature of our sample data:

a) Determine if using a normal distribution or a t distribution for the calculations is appropriate. Hint: consider the sample size.

b) State any assumptions or conditions regarding your sample and/or the population that are necessary for the test procedure you have chosen.

c) Using Statkey, find and record the correct p-value here to 4 decimal places, if the Z- or t- (whatever you chose in a) above) statistic = 3.209.

                                p value =

e) Using a significance level of 3% (alpha = 0.03), state clearly if you reject the null hypothesis or fail to reject the null hypothesis.

Part III

A journalist is writing an article about the results of your investigation and has asked you for a one or two sentence quote to include in the article. The journalist asks “What was the purpose of the investigation? What did you conclude?” Keep in mind that our readers probably never took a statistics course.”

In the space below, write one or two sentences that answer both of the journalist’s questions in a way that is easily understood by the general public AND is consistent with your work in Part II.