In 1998, as an advertising campaign the Nabisco Company announced a \"1000 Chips

Question

In 1998, as an advertising campaign the Nabisco Company announced a "1000 Chips Challenge," claiming that every 18-ounce bag of their Chips Ahoy! cookies contained at least 1000 chocolate chips(Your professor remembers these, gosh he is old). Dedicated Statistics students at the Air Force Academy purchased some randomly selected bags of cookies and counted the chocolate chips. Some of their data are given below. 1219 1214 1087 1200 1419 1121 1325 1345 1244 1258 1356 1132 1191 1270 1295 1135 What is the population of interest? What is the parameter we are trying to learn something about. Are the assumptions and conditions met for performing a hypothesis test and constructing a confidence interval? What would be appropriate hypotheses for a hypothesis test? Calculate a p-value. This p-value is a probability. What is it the probability of? Explain this in the context of this problem. Do you believe Nabisco's claim? Why or why not? Explain. Construct a 95% confidence interval. Explain what the 95% confidence interval means in the context of this problem.

Explanation / Answer

What is the population of interest?

Here population of interest is the number of chocolate chips in 18 ounce  bag of their Chips Ahoy!

What is the parameter we are trying to learn something about.

Here the parameter we are trying to learn is that is there more than 1000 chips in the 18 ounce  bag of their Chips Ahoy!

Are the assumptions and conditions met for performing a hypothesis test and constructing a confidence interval?

Chips bags are randomly selected. The samplling is simple random sampling. Data have a normal distribution as the population size is very high so data can be assumed normal. Data taken are also independent

What would be appropriate hypotheses for a hypothesis test?

H0 : <= 1000 chips

Ha : > 1000 chips

Here is the population mean of chocolate chips available in 18 ounce  bag of their Chips Ahoy!

Calculate a p-value. This p-value is a probability. What is it the probability of?

Here sample mean x = 1238.188

Sample standard deviation s = 94.282

sample size = 16

Test statistic

t = (x - 1000)/ (s/ sqrt(n) = (1238.188 - 1000)/ (94.282 /4) = 10.105

p - value = Pr (t > 10.105; dF = 15) = 2.17 x 10-8 < 0.05

this p - value is the probability of having population mean of chocolate chips less than 1000 for the given population.

Do you believe Nabisco's claim? Why or why not? Explain. Construct a 95% confidence interval. Explain what the 95% confidence interval means in the context of this problem.

Yes, as we reject the null hypotheiss we believe Nabisco's claim.

95% confidence interval = x +- t15,0.05 (s/ sqrt(n) = 1238.188 +- 2.1315 * (94.282/4)

= (1187.95, 1288.43)

Here 95% confidence interval means that if we repeatedly take samples of size 16. There will 95% chance that we will get sample mean in between 95% confidence interval.

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