Sample size, Sampling distribution of proportions
Not what you're looking for?
25) Money magazine reported that the average price of gallon of gasoline in the United States during the first quarter of 2001 was $ 1.46. Assume the price reported by Money is the population mean, and the population standard deviation is $ 0.15.
a) What is the probability that the mean price for a sample of 30 gas stations is within $ 0.03 of the population mean?
b) What is the probability that the mean price for a sample of 50 gas stations is within $ 0.03 of the population mean?
c) What is the probability that the mean price for a sample of 100 gas stations is within $ 0.03 of the population mean?
d) Would you recommend a sample size of 30, 50 or 100 to have at least a 0.95 probability that the sample mean is within $ 0.03 of the population mean?
37.The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries (U.S.A Today, June 21, 1994). Assume the population proportion is p=0.17 and a simple random sample of 800 households will be selected from the population.
a. Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries.
b. What is the probability that the sample proportion will be within plus/minus 0.02 of the population proportion?
c. Answer part (b) for a sample of 1600 households.
Please see attachment file for details
Purchase this Solution
Solution Summary
Answers to 2 questions on Sample size, Sampling distribution of proportions
Solution Preview
Sample size= 30
within plus /minus $0.03
Mean=μ= $1.46
Standard deviation =σ= $0.15
sample size=n= 30
σx=standard error of mean=σ/√n= $0.0274 = ( 0.15 /√ 30)
x1 bar = $1.43 =1.46+0.03
x2bar= $1.49 =1.46-0.03
z1=(x1bar -μ)/σx= -1.0949 =(1.43-1.46)/0.0274
z2=(x2bar-μ)/σx= 1.0949 =(1.49-1.46)/0.0274
Cumulative Probability corresponding to z1= -1.0949 is= 0.1368 0r= 13.68%
Cumulative Probability corresponding to z2= 1.0949 is= 0.8632 0r= 86.32%
Therefore probability that the value of x will be between x1bar= $1.43 and x2 bar= $1.49
is = 72.64% =86.32%-13.68%
Answer: 72.64% or 0.7264
Sample size= 50
within plus /minus $0.03
Mean=μ= $1.46
Standard deviation =σ= $0.15
sample size=n= 50
σx=standard error of mean=σ/√n= $0.0212 = ( 0.15 /√ 50)
x1 bar = $1.43 =1.46+0.03
x2bar= $1.49 =1.46-0.03
z1=(x1bar -μ)/σx= -1.4151 =(1.43-1.46)/0.0212
z2=(x2bar-μ)/σx= 1.4151 =(1.49-1.46)/0.0212
Cumulative Probability corresponding ...
Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency
Tests knowledge of the three main measures of central tendency, including some simple calculation questions.
Know Your Statistical Concepts
Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.
Measures of Central Tendency
This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.
Terms and Definitions for Statistics
This quiz covers basic terms and definitions of statistics.