Question 1
To make the confidence interval, you need to find the mean and the standard deviation for the data.
Since this is a small sample and you don't know the population standard deviation, you will use "t" instead of "z".
Using a t-table you will have to find the value for .01 2tailed test.
Use that value in your formula to calculate the confidence interval.
b) there are several assumptions that you will make including randomness and normality of the data.
Question 2 This deals with % /proportions.
You will use a 1 proportion z to calculate this interval. 95% gives you 5% divided by 2 tails =2.5% or .025. Use the formula to find the standard deviation. You will need p-hat, q-hat and n.
For the last question, there is a formula to find sample size. You are given a .02 margin of error. Assume the confidence interval is still 95%.
Question 1 Production Rates
A manufacturing company wishes to estimate the number of items that its workforce can produce on average each hour now that they have a new machine. The factory examined the records for a random sample of 8 hours over the past month. The hourly production rates for these 8 hours were:
142 175 162 158 190 154 160 185
(a) Calculate by hand and interpret the 99 percent confidence interval for the average number of items produced per hour.
(b) What assumption did you make in order to answer part (a)?
Question 2 Customer Satisfaction
(a) An insurance company wants to estimate the proportion of people unsatisfied with their new telephone help service. A survey of 200 callers revealed 45 were unsatisfied with the service. Construct by hand a 95% confidence interval for the proportion of unsatisfied customers.
(b) If the company wanted to estimate the sample proportion to within 2% of the population proportion, what sample size would be necessary assuming no prior estimate of the proportion is known?
1 answer