Question

a random sample of 75 snowmobiles was selected, and the lifetimes of the batteries in months was measured

1. a random sample of 75 snowmobiles was selected, and the lifetimes of the batteries in months was measured. the sample variance was 8.6. find the 90% confidence interval of the population variance.
2. a recent study of 25 commuters showed that they spent an average of $18.23 on the public transportation per week. if the standard deviation of the sample was $3.00, find the 95% confidence interval; of the population mean. Assume the variable is normally distributed.
3. in a group of 10 men subjected to stress, the mean number of heartbeats per min was found to be 126, and the standard deviation is 4. find the 95% confidence interval of the population mean.
4. daily salaries of substitute teachers for 8 local school districts is shown. what is the point estimate of the mean? What is the 90% confidence interval of the population mean? Daily salaries in dollars are : 60 56 60 55 70 55 60 55
5. We wish to estimate the average salary of workers in the particular field at the 95% confidence level. if the standard deviation is $1050, how large of a sample is needed to be accurate within $200?
6. find the 99% confidence interval for the variance and standard deviation of the weights of 25 gallon containers of motor oil if a sample of 14 containers has a variance of 3.2. the weights are in ounces and you can assume the variable is normally distribute.
7. a study indicated that 29% of women over 55 were widows.
(a) how large of a sample must one take to be 90% confident that the estimate is within 0.05 of the true proportion of women over 55 who are widowed?
(b) if no estimate of the sample proportion is available, how large should the sample be?
8. if the probability of a new-born being female is 0.5, find the probability that in 100 births, 55 or more will be female.
9. 56% of 3 to 5-year old American children are enrolled in a school. If a sample of 500 children is taken, find the probability that at least 250 are enrolled.
10. A researcher feels that the average budget of major city public libraries is $25 million. A random sample of 40 libraries is selected and their annual budgets (in millions of dollars) are shown. @=0.05, is there enough evidence to reject the researcher’s claim?
16.7 17.6 26.5 6.3 16.5 11.9 23.7 14.3 94.0 4.7 11.6 26.5 5.6 58.6 3.2 14.2 3.5 10.9 11.8 15.2 30.1 19.7 11.7 38.8 36.3 4.8 7.9 14.2 18.0 24.5 69.2 8.5 19.2 5.0 15.6 41.0 27.1 10.3 3.7 13.6
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