Question

In: Statistics and Probability

A random group of 50 bowlers had an average score of 189. The standard deviation of...

A random group of 50 bowlers had an average score of 189. The standard deviation of all bowlers in the league was 9.1. Assume the population has a normal distribution. Find the margin of error, and then find the 95% confidence interval for the population mean

Solutions

Expert Solution

Solution :


Given that,

Point estimate = sample mean =     = 189

Population standard deviation =    = 9.1

Sample size n =50

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96* ( 9.1 / 50 )

Margin of error = E = 2.5224
At 95% confidence interval estimate of the population mean
is,

- E < < + E

189 - 2.5224 <   <189 + 2.5224

186.4776<   < 191.5224

( 186.4776, 191.5224)


Related Solutions

A company has 189 accountants. In a random sample of 50 of them, the average number...
A company has 189 accountants. In a random sample of 50 of them, the average number of overtime hours worked in a week was 9.7 and the sample standard deviation was 6.2 hours. a) Find a 95% confidence interval of the average number of overtime hours worked by each accountant in this company during that week. b) Find a 99% confidence interval of the total number of overtime hours worked by each accountant in this company during that week.
The average score for games played in the NFL is 22.4 and the standard deviation is...
The average score for games played in the NFL is 22.4 and the standard deviation is 9.1 points. 43 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. A. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) B. What is the distribution of ∑x∑x? ∑x∑x ~ N(,) C. P(¯xx¯ > 22.3185) = D. Find the 60th percentile for the mean score for this sample size. E. P(21.0185 < ¯xx¯ <...
The average score for games played in the NFL is 21 and the standard deviation is...
The average score for games played in the NFL is 21 and the standard deviation is 9.3 points. 10 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the distribution of ∑x∑x? ∑x∑x ~ N(,) P(¯xx¯ < 20.9887) = Find the 70th percentile for the mean score for this sample size. P(20.5887 < ¯xx¯ < 23.3705) = Q1 for the...
The average score for games played in the NFL is 22 and the standard deviation is...
The average score for games played in the NFL is 22 and the standard deviation is 9 points. 13 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the distribution of ∑x∑x? ∑x∑x ~ N(,) P(¯xx¯ > 19.1557) = Find the 72th percentile for the mean score for this sample size. P(20.0557 < ¯xx¯ < 25.0481) = Q1 for the...
The average score for games played in the NFL is 20.7 and the standard deviation is...
The average score for games played in the NFL is 20.7 and the standard deviation is 9.3 points. 49 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the distribution of ∑x∑x? ∑x∑x ~ N(,) P(¯xx¯ < 21.7071) = Find the 68th percentile for the mean score for this sample size. P(19.6071 < ¯xx¯ < 21.9643) = Q3 for the...
A. The average SAT score of students is 1110, with a standard deviation ≈ 120. If...
A. The average SAT score of students is 1110, with a standard deviation ≈ 120. If a sample of n = 25 students is selected, what is the probability that the sample mean would be > 1150? That is, what is p(M>1150)? B. Which of the following will decrease statistical power? SELECT ALL THAT APPLY. a smaller sample size a larger effect size a larger standard deviation a larger alpha
The average score for games played in the NFL is 22.2 and the standard deviation is...
The average score for games played in the NFL is 22.2 and the standard deviation is 8.9 points. 12 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ N(,) What is the distribution of ∑ x ∑x ? ∑ x ∑x ~ N(,) P( ¯ x x¯ > 19.7462) = Find the 65th percentile for the mean score...
3. The national mean score of an aptitude test is 50 with a standard deviation of...
3. The national mean score of an aptitude test is 50 with a standard deviation of 5. I think students at Ohio University can earn higher scores than people nationally. I survey 30 students at Ohio University and find a mean 57 with a standard deviation of 6.8. Is the mean scores of Ohio University students significantly more than the mean score of the aptitude test nationally? (use  = .05) a. State the null and alternative hypotheses in symbols....
Historically, the average score of PGA golfers is 67.69 with a standard deviation of 2.763. A...
Historically, the average score of PGA golfers is 67.69 with a standard deviation of 2.763. A random sample of 50 golfers is taken. What is the probability that the sample mean is between 67.57 and 67.69? 1) 0.0173 2) 0.0469 3) 0.8795 4) 0.1205 5) The sample mean will never fall in this range.
A Population has a mean of 50 and a standard deviation of 15. If a random...
A Population has a mean of 50 and a standard deviation of 15. If a random sample of 49 is taken, what is the probability that the sample mean is each of the following a. greater than 54 b. less than 52 c. less than 47 d. between 45.5 and 51.5 e. between 50.3 and 51.3
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT