Question

In: Statistics and Probability

A pizza shop owner wishes to find the 95% confidence interval of the true mean cost...

A pizza shop owner wishes to find the 95% confidence interval of the true mean cost of a large plain pizza. How large should the sample be if she wishes to be accurate to within $0.14 ? A previous study showed that the standard deviation of the price was $0.40. Round your final answer up to the next whole number.

Solutions

Expert Solution

Given that Margin of error = $0.14

Given Standard Deviation = $0.4

Given Confidence level = 95% = 0.95

= 1 - confidence level

= 1 - 0.95

= 0.05

/2 = 0.025

Z/2 will be z-score that has an area of 0.025 to its right or 0.975 to its left

Z/2 = 1.96 from the below attached table

Margin of error = Z/2 * ( / )

Where n is the sample size

0.14 = 1.96 * (0.4 / )

= (1.96 * 0.4) / 0.14

= 0.784 / 0.14

= 5.6

squaring on both sides we have

()2 = 5.62

n = 31.36

So n = 32 rounded up to the next whole number


Related Solutions

Find the 95% confidence interval of the mean of a vector in r code. The vector...
Find the 95% confidence interval of the mean of a vector in r code. The vector length is 100.
Find a 95% confidence interval for predicting the mean length of fish in a particular pond...
Find a 95% confidence interval for predicting the mean length of fish in a particular pond if the sample data contained the following length in centimeters 23 45 43 34 26 36 67 45 43 55 53 42 87 65 45 51 53 54 54 48 49 54 53 52 54
Find the margin of error for a 95% confidence interval (nearest hundredths) of the mean test...
Find the margin of error for a 95% confidence interval (nearest hundredths) of the mean test score of Statistics students at Clayton State University given the following sample data scores: 87 85 56 82 67 77 73 71 90 74 76 79 81 84 Find a 99% confidence interval estimate (nearest hundredth) using the data in #12. The height (in inches) of males in the United States is believed to be Normally distributed, with mean µ. The average height of...
calculate the range for the expected true mean temperature with 95% confidence (2-sided confidence interval) calculate...
calculate the range for the expected true mean temperature with 95% confidence (2-sided confidence interval) calculate the value the true mean temperature should be greater than with 95% confidence (1-sided confidence interval) What is the difference between these two problems? what equation do I use?
What does a 95% confidence interval mean?
What does a 95% confidence interval mean?
95% Confidence Interval: 86.19 ± 0.364 (85.8 to 86.6) "With 95% confidence the population mean is...
95% Confidence Interval: 86.19 ± 0.364 (85.8 to 86.6) "With 95% confidence the population mean is between 85.8 and 86.6, based on 33945 samples." Short Styles: 86.19 (95% CI 85.8 to 86.6) 86.19, 95% CI [85.8, 86.6] Margin of Error: 0.364 What is the impact of your margin of error on your findings? Explain. Is there enough evidence to reject the null hypotheses, explain in plain English?
2.         a.         Find a 98% confidence interval for the true mean of a population if a sample of     ...
2.         a.         Find a 98% confidence interval for the true mean of a population if a sample of                  52 results in a mean of 100. Assume the population standard deviation is 12. b.        Assume now that the same results occurred, the population was normal, and the             sample size was reduced to 10. c.        Repeat problem 2b assuming that the population standard deviation was unknown, and              “s” was 12.
Use the given data to find the 95% confidence interval estimate of the population mean μ...
Use the given data to find the 95% confidence interval estimate of the population mean μ . Assume that the population has a normal distribution. IQ scores of professional athletes: Sample size n=25 Mean=103 Standard deviation s=15 Answer: ____ <μ< _____
Use the given data to find the 95% confidence interval estimate of the population mean μ....
Use the given data to find the 95% confidence interval estimate of the population mean μ. Assume that the population has a normal distribution. IQ scores of professional athletes: Sample size n=20 Mean x¯¯¯=104 Standard deviation s=14 <μ<
True or False 1. A 95% confidence interval of {-.5, 3.5} means that, on 95% of...
True or False 1. A 95% confidence interval of {-.5, 3.5} means that, on 95% of repeated experiments, the sample mean will be between -.5 and 3.5. 2. The probability of making a type-I error depends, in part, on power. 3. In general, 4. According to the central limit theorem, the sample mean, , is always normally distributed, even when population distribution of x is not normal
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT