Posted: December 30th, 2016

# Two students are eating a bag of Doritos tortilla chips, nacho cheese flavor. They quickly devour the little bag and one of the students says I think they under filled our bag, seems to me it used to take longer to fininh a bag like that.

Two students are eating a bag of Doritos tortilla chips, nacho cheese flavor. They quickly devour the little bag and one of the students says I think they under filled our bag, seems to me it used to take longer to fininh a bag like that. The other student, clearly the teacher s pet in statistics class says, we can statistically test your claim that they under filled this bag. In fact, we can test whether Frito Lay might be just under filling their bags these days. It says right here on the bag that it contains 269.3 grams.
After going on line the two students find out that indeed, Frito Lay does claim that their bags are filled with 269.3 grams of chips, though they do admit that there is some unavoidable error or variation from bag to bag. In fact, the students find that the standard deviation is 0.523 grams.
Putting into practice what they ve learned in statistics class, the students buy eight bags of the Dorito tortilla chips. I think we can assume that we have a reasonable random sample of bags though we can t be totally sure of this, says one of the students. They then go to one of their friends who is a chem major and use the chem lab scales to weigh exactly each of the eight bags. OK now, we need to take the mean of the weights for the eight bags just like professor Schmoozmore told us to do, says one of the students to the other. The mean turned out to be 269.85. I can t believe this, the mean of our sample is actually larger than what Frito Lay says it should be! They claim that they fill them with 269.3 grams. The other student, clearly less interested in the whole project says, I m sure glad we went ahead and bought eight bags, I was really craving some Doritos. Yeah whatever, says the other student, but this is really interesting, I think we can assume that 259.3 grams is the population mean mu and the population sigma is 0.523 and now we can run our z test since using our sample mean of 269.85 and test the null hypothesis,
Which of the following statements best defines the null hypothesis the students wish to test?

4. To see if the mean weight of 269.3 should really be below the weight of their eight bags
1. The mean weight of their eight bags is just a random sample from the population of bag weights whose mean is 269.3 grams.
2. The mean weight of their eight bags should be below the population mean weight of 269.3 grams.
3. The mean weight of the eight bags shows that the students got cheated by Frito Lay
4. To see if the mean weight of 269.3 should really be below the weight of their eight bags

Logically speaking, if the students are only worried that they got cheated and were suspicious that Frito Lay was actually undertaking a policy of underfilling the newer bags, which type of test should they use?
1. A two tailed test
2. A one tailed test for sample means above the population mean
3. A one tailed test for sample means below the population mean
4. It doesn t matter, a one or two taile test will both answer their question just as well

Another way of stating the null hypothesis the students are testing is:
1. The population mean mu is > their sample mean
2. The population mean mu is < their sample mean
3. The students sample mean is either greater than or less than the population mean mu
4. The students have sampled from a population of tortilla chip bags whose mean is equal to the stated population mean by Frito Lay
Since the students are using a sample of eight Dorito chip bags and taking the mean of the weight of the bags they must utilize a sampling distribution of means. What is the standard deviation of this sampling distribution of means for their purposes?
1. 0.339 grams
2. 0.095 grams
3. 0.185 grams
4.
1.05 grams

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