Question

A simple random sample of 20 cars in the drive-thru of a popular fast food restaurant had an average bill of $18.21 per car. Suppose the distribution of the drive-thru bills is distributed normally with a standard deviation (σ) of $5.89 per car.

Constructing a (90%, 95% , or 99%) confidence interval for the µ. a: How do you explain µ? or What is µ in your study? What are you looking for? b: What confidence level have you chose? c: What is the lower and upper boundary of the confidence interval you have constructed? d: Interpret the CI you calculated in part ”c” based on the study you’re working on? e: What is the margin of error in your calculation? f: What was the sample size in the study you’re working on? g: Let’s have a new margin of error: Increase the margin of error a little bit.

What is the new margin of error of your choice? h: Now you have increased the margin of error based on this new margin of error how should the new sample size change? Increase or decrease, and why do you think this will happen? i: Now calculate the new sample size based on the new margin of error you proposed. Assume that σ, confidence level haven’t change. What is the new sample size? j: Is this new sample size that you calculated in part ”I” matching your assumption in part ”h”? Again, why is this happening? Make a claim on µ based on your study and what you got from ”Part I.c” and name it Alternative hypothesis. This is the Ha b: What is the (µ0) in your claim? c: State the Null (H0) and Alternative (Ha) Hypotheses in mathematical notation. d: what test statistic are you using ? Calculate the test statistic. e: Calculate the P-value and explain why have you calculated in this way? f: Suppose the level of significant is an α = 0.01. Interpret the result of this study based on the p-value and alpha. You should explain if you are rejecting or not rejecting your claim. g: Suppose the level of significant is an α = 0.05. Interpret the result of this study based on the p-value and alpha. You should explain if you are rejecting or not rejecting your claim. h: What is the relation between the result in ”Part I.d” and ”Part II.g & Part II.h”

Answer 1

Dear student, we can provide you with the solution of 4 sub question at a time.

the bill of the drive thru fast food restraunt

a) is the population mean of the bill of the drive thru fast food restraunt.

b) Above we have calculated all the three confidence interval but 95% would be moe appropriate.

c) Lower boundary is $15.63

upper boundary is $ 20.79

d) We are 95% confidentthat the population mean bill of the drive thru fast food restraunt lie within the interval calculated above which is ($15.63 , $20.79)

e) Margin of error is

f)

sample size is n = 20

g) let the Margin of error be 3.58

h) Yes the sample size should change for the same population standard deviation and confidence level.

i) new sample size is