Please answer ONLY F and G. Thank you!! 1. A spinach producer is testing a new p

Question

Please answer ONLY F and G. Thank you!!

1. A spinach producer is testing a new packaging line. They want the mean weight of spinach in each package to be 8 ounces. If the mean is too high, they will lose money, and if the mean is too low, customers will get angry. They run the machine for a few days to get a large population of packages, then select 12 packages at random and weigh the spinach in each. If they find strong evidence the mean is too high or low, they can recalibrate the machine. Here are the sample weight (in ounces): 7.7, 6.8, 8.0, 7.4, 7.1, 7.4, 7.2, 7.3, 8.3, 7.7,7.6,7.0 (Except for the graph(s), I recommend doing this problem with a calculator and table as practice for exams. You may check your answers with R if you wish.) (a) State hypotheses appropriate to the research question. (b) Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you? (c) Choose an appropriate test statistic for this situation and justify your answer. Then compute the observed value of the test statistic for this data. (d) Find the rejection region if we desire a test with 0.01. (e) Make a reject or not reject decision. Then state your conclusion in the context of the problem. In other words, does it seem the packaging line needs recalibrating, and if so, in which direction? (f) If you calculated a 99% confidence interval for the population mean weight, would you expect it to contain 8? Why or why not? (g) Find a 99% confidence interval for the population mean weight.

Explanation / Answer

f)

Yes, because hypotheis is given that the mean weight of spinach in each package to be 8 ounces. So, it should to be contain 8

g)

CI for = 99%

n = 12

mean = 7.4583

t-value of 99% CI = 3.1058

std. dev. = 0.4274

SE = std.dev./sqrt(n) = 0.12338

ME = t*SE = 0.38319

Lower Limit = Mean - ME = 7.07511

Upper Limit = Mean + ME = 7.84149

99% CI (7.0751 , 7.8415 )

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