Question

A car manufacturer is going to introduce a new model in the market. The production process is so set that the mpg highway of the new model has a population mean μ mpg with a population standard deviation of 2.5 mpg. Based on 14 trials, a researcher estimates the mean mpg (μ) with a confidence interval of (23.271, 25.469).

1. Does the researcher need any assumption to compute the confidence interval for μ?
a) No, we do not require any assumption, because the sample size n is large.
b) No, we do not require any assumption, because the population standard deviation σ is known.
c) Yes, we assume the population is normally distributed, because the sample size n is small.
d) Yes, we assume the population is normally distributed, because the population standard deviation σ is known.
e) No, we do not require any assumption, because the sample size n is small.

2. What is the confidence level (in %) of the interval (23.271, 25.469)? [Do not type the % symbol]

A: 81

B: 87

C: 89

D: 90

E: 93

F: 96

3. The minimum number of sample required to estimate μ within a margin of error 0.330 with 95% confidence is:

A: 89

B: 219

C: 220

D: 221

E: 222

F: 223

Answer 1

1)

c) Yes, we assume the population is normally distributed, because the sample size n is small.

2)

margin of error =(upper limit-lower limit)/2=

1.099

since margin of error E =z*σ/√n

1.099 =z*2.5/sqrt(14)

z =1.099*sqrt(14)/2.5 =1.645

above z score is for confidence interval of 90%

option D is correct

3)

for95% CI crtiical Z          =	1.960	from excel:normsinv(0.975)
standard deviation σ=	2.500
margin of error E =	0.33
required n=(zσ/E)2 =	221	Rounding up

option D is correct