Question

2. Industrialist H.E. Pennypacker wants information on the customers that patronize his bicycle stores. He surveyed 81 randomly-selected individuals who made a purchase at his Pasadena store to find out how much they spent, on average. The mean amount spent was $62 with a standard deviation of $15.

a) What is the population in this study?

b) Construct a 95% CI for the mean amount of money an individual spends at the Pasadena store. Explain the meaning of this CI (i.e., what does it say about the parameter of interest?).

c) Construct a 99% CI for the mean amount of money spent at the Pasadena store. Contrast this interval with the one from b and explain why it is different.

d) Suppose 100 people were initially surveyed, but 19 of them actually refused to answer (leading to the final sample size of 81). If the 19 individuals who refused to answer spent considerably less money than the 81 who did respond, how would this affect the estimate of the mean and the CI?

Answer 1

given that

Sample size =n=81

Mean =m=62

SD=S=15

a)

Here population in study is customers that patronize H.E pennypacker bicycle store

b)

Interpretation: we construct 100 such 95% confidence intervals for mean spending then 95 times we will get the population mean will lie within those intervals.

c)

Width of this interval is smaller than that in part (b) so it's give more close value of parameter mean than than that given by part (b)

d)

If the spending of 19 customers is very less compared to 81 then there is decrease in the sample mean but increase in variation but as they haven't answered so we create CI on the basis of only 81 so there is no effect of 19 who haven't answered.