Question 1
Design a 95 percent confidence interval for the proportion of defectives in a large lot, if a sample of 200 showed 12 defectives.
Question 2
The prices of 23” TV sets sampled by a consumer guide were as follows: $400, $600, $550, $450, $700, $500, and $650. Build a 98 percent confidence interval for the mean.
Question 3
You wish to estimate with 95 percent confidence the proportion of families that own two cars.
a) How large a sample do you need if you allow an error of up to 2 percent in each direction?
b) What will be the sample size if your prior estimate for p was 0.7?
Question 4
A sample of 400 people getting a tax refund showed the mean to be $900 and standard deviation to be $200.
a) Design a 99 percent confidence interval.
b) How large a sample do you need if you want the error to be no more than $10?
Question 5
The weight of bags “checked in” is normal, with a mean of 30 pounds and a standard deviation of 9 pounds.
a) What is the probability that a randomly selected bag will weigh more than 48 pounds?
b) What is the probability that the total weight of 4 bags will be more than 192 pounds?
c) Find the probability that a sample of 81 bags will average more than 32 pounds.
d) If a sample of 36 bags showed the mean to be 33 pounds, can you conclude that the average weight has changed? (use alpha = 0.05)
Question 6
Test the hypothesis that more than 60 percent of the U.S. senators (of a total 100 senators) favor the president’s economic plan, if a sample of 40 showed that 22 favor the plan (use alpha = .05).
Question 7
The salaries of five employees at XYZ Brokerage are $30,000, $50,000, $60,000, $70,000, and $90,000. The industry salaries are normal, with a mean of $55,000 and standard deviation of $8,000. Can you conclude with a 5 percent level of significance that the salaries of workers in XYZ Brokerage are higher than that for the industry?
Question 8
The number of accounts handled by a new company over the last six years has been 80,000, 140,000, 90,000, 110,000, 140,000, and 100,000, respectively. Forecast for the seventh period using linear regression. Find R-squared and note if your model is good or not.
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