Hypothesis testing and probability problems

1. After a sample of numbers is taken from a population, the 95% confidence interval is calculated out at {10.5, 12.0}
What is the correct way to interpret this confidence interval? Choose one. (1 point)

A) 95% of all values in the population are between 10.5 and 12.0
B) The true population mean has to be between 10.5 and 12.0
C) There is a 95% probability that the true population parameter is between 10.5 and 12.0.
D) The mean is between 10.5 and 12.0, and the standard deviation is 95.

2. A sample is taken prior to a major Election of likely voters. The null hypothesis is that the votes will be split 50/50. One candidate gets 54% of the support in the sample, and the P-value for this sample is calculated to be 0.12. What is the correct interpretation of the P-value? (1 point)

A) Assuming that the true percentage actually supporting the candidate is 50%, there is a 0.12 probability that a sample will show results of 54% or greater.
B) There is a 95% probability that the true population percentage is 54% plus/minus 12%.
C) The candidate has only a 12% chance of loosing the election.
D) 12% of the votes in the upcoming election are uncertain, the rest can be estimated.

3. An engineer in a widget factory wants to make a change to the process, and to switch to a cheaper supplier of the crucial raw material in the manufacture of widgets (that is, of course, widgeterium). It is important that the weight of the finished widgets not be different from the specified weight of 10 grams. A sample of 40 widgets created on a test run of the new material has an average weight of 10.8 grams, with a standard deviation of 2. Do the following (show your work in order to get partial credit on partially correct answers):
a. Identify the null and alternative hypothesis (0.5 points)
b. Calculate the proper test statistic (0.5 points)
c. Calculate the proper P-value (0.5 points)
d. In plain English, properly interpret the results, using a significance level of 0.05. (0.5 points)

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