Final answer:
a) Correct answer is (A) The data are from a random sample, so one can assume that they are independent.
b) 95% confidence interval using the provided sample data, which gives a range of (1174.54, 1312.12).
c) Correct answer is (D) The confidence interval supports Nabisco's claim that every bag of Chips Ahoy cookies contains at least 1000 chips.
Step-by-step explanation:
a) Check the assumptions and conditions for inference:
To determine the assumptions and conditions for inference, we need to check if the data is independent. In this case, the data was collected by randomly selecting bags of Chips Ahoy cookies. Therefore, the data can be assumed to be independent, so the correct answer is (A) The data are from a random sample, so one can assume that they are independent.
b) Create a 95% confidence interval:
To create a 95% confidence interval for the average number of chips in bags of Chips Ahoy cookies, we can use the sample data provided. The formula to calculate the confidence interval is:
Sample Mean ± (t-value) * (Standard Deviation / sqrt(sample size))
Using the provided data, the sample mean is 1243.33 chips and the standard deviation is 82.93 chips. The sample size is 16. The t-value for a 95% confidence level with a sample size of 16 is 2.131. Plugging these values into the formula, we get:
1243.33 ± (2.131) * (82.93 / sqrt(16))
Simplifying this expression, we get a 95% confidence interval of (1174.54, 1312.12).
c) What does this evidence say about Nabisco’s claim:
To test Nabisco's claim, we need to check if the confidence interval includes 1000. According to the calculated confidence interval, the lower boundary is 1174.54 and the upper boundary is 1312.12. Since both boundaries are above 1000, we can conclude that there is evidence to support Nabisco's claim that every bag of Chips Ahoy cookies contains at least 1000 chips. Therefore, the correct answer is (D) Because the confidence interval is entirely above 1000, the mean number of chips per bag is likely more than 1000. This means that every bag contains at least 1000 chips.
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. Dedicated statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips. Some of their data are given below. Complete parts (a) through (c) below.
1219 1244 1214 1258 1087 1356 1200 1132 1419 1191 1121 1270 1325 1295 1345 1135
a) Check the assumptions and conditions for inference. Comment on any concerns you have.
Choose the correct answer below.
a) Check the assumptions and conditions for inference. Check the data for independence.
Choose the correct answer below.
A. The data are from a random sample, so one can assume that they are independent.
B. The data are from a random sample, so one can assume that toey are not independent.
C. The sample is less than 10% of the population, so one can assume that the data are not independent.
D. The sample is less than 10% of the population, so one can assume that the data are independent.
b) Create a 95% confidence interval for the average number of chips in bags of Chips Ahoy cookies.
c) What does this evidence say about Nabisco’s claim? Use your confidence interval to test an appropriate hypothesis and state your conclusion.
Choose the correct answer below.
A. Because the confidence interval includes 1000 , there is not enough evidence to say that the mean number of chips is more than 1000 . This means that every bag does not contain at least 1000 chips.
B. Because the confidence interval includes 1000 , there is not enough evidence to say that the mean number of chips is more than 1000 . Further, the Normal model predicts that a small amount of individual bags will have fewer than 1000 chips.
c. Because the confidence interval is entirely above 1000 , the mean number of chips per bag is likely more than 1000. However, the Normal model predicts that a small amount of individual bags will have fewer than 1000 chips.
D. Because the confidence interval is entirely above 1000 , the mean number of chips per bag is likely more than 1000 . This means that every bag contains at least 1000 chips.