3. This is a “quality control\" problem. You manage several grocery stores and a
ID: 347639 • Letter: 3
Question
3. This is a “quality control" problem. You manage several grocery stores and are concerned that one of them may be failing to monitor their produce properly. This grocery store sells 5-pound bags of whole potatoes. You know that there will be variability; some bags will weigh more than others. You also know that you will lose profits if the bags weigh too much, but it would be illegal if the bags weighed too little. The mean across all stores is 5 pounds and the population standard deviation is 1 pound. So you take a sample of 16 bags of potatoes from that store and you find the average weight of that sample is 6 pounds. Please create a 95% confidence interval to estimate whether this store is over or under-filling their bags of potatoes. a) Would you use a z-score or a t-score for this confidence interval? (Hint: do you know the population variability?) b) What would your critical z-score be? c) What would your standard error of the mean be?. d) Given that the average weight from our sample is 6 pounds and the standard error of the mean of 0.25: Calculate the lower boundary of your confidence interval: Calculate the upper boundary of your confidence interval: e) Does the “ideal weight” of 5 pounds fall within that range? f) What advice would you give the manager of that particular store? g) You would use az score of to construct a 95% confidence interval, and a z-score _to construct a 99% confidence interval of h) What is the point estimate for of the population mean?Explanation / Answer
a) We will use Z-score as we know population standard deviation
b) level: 100% – 95% = 5%.
/2 = area in each tail = 0.025
area in the middle = 1 – 0.025 = 0.975
Critical z-value = 1.96 (using Z chart and finding corresponding value of 0.975)
c) Standard error of mean (SEM) = Standard deviation / root of sample size = 1 /root of 16 = 1/4 = 0.25
d) Confidence interval = Mean +/- Z*SEM
where Z = 1.96 for 95% interval
Using above formula, Lower boundary = 5.51
Upper bound = 6.49
3) No, the ideal weight of 5 pounds is not withing range.
f) I would advice store manager to check the weighing process of bags of potatoes as the range of weight 5.51-6.49 is way above the average across stores.
g) Z-score of 1.96 at 95% and 2.575 for 99%
h) Mean weight of samples in population = Point estimate = 5 pounds
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