below. a. Compute a 93% confidence interval for μ, the average weight of these bags of chips. Round the answers to at least five decimals if necessary Lower/smaller bound: ____________ grams Upper/larger bound: ___________ grams b. Interpret the interval calculated in part a. We are _____________% confident that the average weight of: A. all Brand A bags of chips B. this sample of Brand A bags of chips is: A. captured by B. not captured by the upper and lower bounds of the interval in part a. c. Instead of the current confidence level of 93%, suppose we were to decrease the confidence level to 91% and use that to compute a new confidence interval. If all other values/quantities stayed the same, how would the width of this new interval compare to the width of the interval computed in part a.? The new interval would be narrower The new interval would be wider The new interval would be the same width There is not enough information provided to determine how this would affect the interval wid
As a way to assess quality control, a product tester for Brand A wishes to estimate the average amount of chips (by weight) in the standard size chip bags produced by Brand A. The tester takes a random sample of 31 bags of chips and finds the average weight to be x= 209.11 grams. Suppose the known population standard deviation of the weight of these bags of chips is σ= 3.27 grams. Use this information to answer the questions below.
a. Compute a 93% confidence interval for μ, the average weight of these bags of chips. Round the answers to at least five decimals if necessary
Lower/smaller bound:
____________ grams
Upper/larger bound:
___________ grams
b. Interpret the interval calculated in part a.
We are _____________% confident that the average weight of:
A. all Brand A bags of chips
B. this sample of Brand A bags of chips
is:
A. captured by
B. not captured by
the upper and lower bounds of the interval in part a.
c. Instead of the current confidence level of 93%, suppose we were to decrease the confidence level to 91% and use that to compute a new confidence interval. If all other values/quantities stayed the same, how would the width of this new interval compare to the width of the interval computed in part a.?
- The new interval would be narrower
- The new interval would be wider
- The new interval would be the same width
- There is not enough information provided to determine how this would affect the interval width
d. The tester also takes a similar sample of bags of chips from a competitor, Brand B, and measures the weight of product in these bags as well. The 93% confidence interval for the average weight of Brand B bags of chips is (197.1352, 199.4848). Based on this result, what can we say about the average weight of bags of chips from Brand A versus the average weight of bags of chips from Brand B? compare this confidence interval with the one you calculated in part a.
- The average weight of Brand A bags of chips is significantly lower than the average weight of Brand B bags of chips
- There is no significant difference in the average weight of Brand A bags of chips versus Brand B bags of chips
- The average weight of Brand A bags of chips is significantly higher than the average weight of Brand B bags of chips
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