Submarine Sandwiches with Pizzazz : Your advertising campaign has worked out so
ID: 3337195 • Letter: S
Question
Submarine Sandwiches with Pizzazz: Your advertising campaign has worked out so well for your pizza deliveries that you would now like to promote your restaurants submarine sandwiches. So you are considering offering a $1 off coupon on subs to increase the amount of submarine sandwiches you are selling each week. However, you are unable find the total number of subs sold each week anywhere on your computer and no way for you to total them up without going through the sales records one by one. Never fear! Since you have now learned about confidence intervals in your Statistics class you can get an estimate for the mean number of subs sold each week by taking a random sample of 36 weeks and calculating the number of subs sold during those weeks. Your random sample resulted in a mean of 7.25 sub sandwiches per week. Assume you have a population standard deviation of 2.5.
(a) Construct a 95% confidence interval for mean number of submarines sandwiches sold each week. (Hint: Z-interval) Round 3 decimal.
Interpret the interval.
(b) Construct a 98% confidence interval for the mean number of submarine sandwiches sold each week. (Hint: Z-interval) Round 3 decimals.
What effect did increasing the level of confidence have on the interval? (Hint: Compare your answers for part (a) and (b). Did the interval get wider or narrower?)
(c) How many weeks should you include in your sample if you want your estimate for the mean number of submarine sandwiches sold each week to be within 0.5 sub sandwiches with 99% confidence?
Explanation / Answer
here std error of mean =std deviation/(n)1/2 =2.5/(36)1/2 =0.4167
a) for 95% CI ; z= 1.96
therefore 95% confidence interval for mean =sample mean -/+ z*std error =6.433 ; 8.067
Interpretation: above interval gives 95% confidence to contain true population mean number of submarines sandwiches sold each week.
b) for 98% CI ; z =2.3263
therefore 98% confidence interval for mean =sample mean -/+ z*std error =6.281 ; 8.219
effect : interval get wider
c)
for 99% CI ; z=2.5758
margin of error E =0.5
hence required sample size n=(z*std deviation/E)2 =~166