In an effort to estimate the mean amount spent per household per month in a small Canadian town, data were collected for a sample of 50 households. The sample showed an average amount of $2000 and a standard deviation of $500.

a.
Develop a 90% confidence interval estimate of the population mean amount spent.

b.
Develop a 95% confidence interval estimate of the population mean amount spent.

c.
Discuss what happens to the width of the confidence interval as the confidence level is increased. Does this seem reasonable? Explain.

d.
If the data were collected for a sample of 20 households rather than 50, develop a 95% confidence interval estimate of the population mean amount spent, assuming the population has a normal probability distribution.

e.
Discuss what happens to the width of the confidence interval as the sample size is decreased. Does this seem reasonable? Explain.

Solution Preview

Hello,

The formula would be: C. I. = M ± (z * SE)
Where:
m=mean
z = the degree of alpha - we get it from a z-table: http://www.statsoft.com/textbook/sttable.html#z
SE = standard error

to get SE = standard deviation / square root of sample size

A. 90% confidence interval = our z score would be 1.65

... a.) Construct a 95% confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and the week ...

... explanation is given explaining how to calculate point estimate of population proportion, how to calculate Margin of Error at 95% confidence interval, and 95 ...

Calculating Standard Deviations and Confidence Intervals. ... (a) Calculate the mean, standard deviation, and confidence interval for menu preference assuming ...

... Step 5: Calculate the confidence interval Confidence interval from ... After surveying employees, the staff calculated that a 95% confidence interval for the ...

... 2 tailed test because we are calculating the confidence...Calculates Confidence interval for true average degree of ...Calculate the mean and standard deviation of ...

Calculate probability, building confidence interval and ... Hence, a 95% confidence interval for mean time is ... detailed steps on calculating probability, building ...

... to construct the confidence intervals and calculate the probabilities ... The sample value X is calculated. ... will use z-value to construct the confidence interval. ...

...Calculate the confidence interval. Interpreting the results. Please see the attachments. ... Test Statistic used is = 2.005185976 Calculate the confidence interval. ...