Section 7 -3: Estimating a Population Standard Deviation o, using the Sample Standard Deviation s, . 1. State the condition that is required before we can use the normal distribution to estimate a population mean u, if the sample standard deviation s, is known. 2. What is the best point estimate for the population standard deviation of ? 3. Label the value for the Degrees of Freedom and the critical values for x and XR that correspond to the given confidence level and degrees of freedom. 3A) A confidence level of 99% with n = 26 3B) A confidence level of 98% with n = 41 Degrees of Freedom = Degrees of Freedom = XL = XR = XL = XR = 3C) A confidence level of 98% with n = 61 3D) A confidence level of 95% with n = 27 Degrees of Freedom = Degrees of Freedom = XL = XR = XL = XR =3E) A confidence level of 90% with n = 51 3F) A confidence level of 99% with n = 23 Degrees of Freedom = Degrees of Freedom = XL = XR = Xi = XR = 3G) A confidence level of 90% with n = 31 3H) A confidence level of 98% with n = 24 Degrees of Freedom = Degrees of Freedom = xi = XR xi = XR = 4. Construct a confidence interval for the true value of the population standard deviation or if the population is normal. Show the set-up and answer, Round to 2 decimal places. 4A) n=41, s, = 1.83 , Confidence Level = 99% Confidence Interval set up: Confidence Interval:4B) n=31, s, =5.72 Confidence Level = 95% Confidence Interval set up: Confidence Interval: 4C) n= 23 s, = 1.28 Confidence Level = 90% Confidence Interval set up: Confidence Interval: 4D) n= 71, s, =4.8 Confidence Level = 98% Confidence Interval set up: Confidence Interval:5. Math SAT scores for women form a normal distribution. A sample of 31 women's scores had a mean of 600 points and a standard deviation of 80 points. Find a 95% confidence interval for the population standard deviation o, in women's math SAT scores. n= Confidence Level = Confidence Interval set up: Confidence Interval: Confidence Interval Statement: I am _% confident that the true population standard deviation or, of the Math SAT scores for women students is between 6. Weights for women police officers form a normal distribution. A sample of 27 women' police officers weight's had a mean of 145 pounds and a standard deviation of 2.4 pounds. Find a 99% confidence interval for the population standard deviation o, in women police officers weights. Confidence Interval set up: Confidence Interval: Confidence Interval Statement: I am _ % confident that the true population standard deviation o, of the Weights for women police officers is between7. Adult reading rates form a normal distribution. A sample of 81 adults showed an average reading rate of 100 words a minute and a standard deviation of 15 words a minute. Find a 90% confidence interval for the population standard deviation o, of adult reading rates. Confidence Interval set up: Confidence Interval: Confidence Interval Statement: I am _ % confident that the true population standard deviation o, of adult reading rates is between 8. The width of men's hips form a normal distribution. 41 men were selected at random. The men had an average hip width of 18 inches with a standard deviation of .75 inches. Find a 98% confidence interval for the population standard deviation o, in the width of men's hips. Confidence Interval set up: Confidence Interval: Confidence Interval Statement: I am % confident that the true population standard deviation o, of adult reading rates is between9. The number of pull-ups a grade school students can do in 5 minutes forms a normal population. A simple random sample of students was taken and the number of pull-ups each student did in 5 minutes is shown below. Find a 95% confidence interval for the population standard deviation in the number of pull-ups grade school students can do in 5 minutes 3 6 6 6 7 9 g 9 10 12 12 12 12 12 12 12 15 15 15 15 15 15 15 15 n = Confidence Interval set up: Confidence Interval: Confidence Interval Statement:Sample Size 10. Find the minimum sample size required to be 95% confident that the sample standard deviation s, is within 10% of the true population standard deviation o. The population is normal. 11. Find the minimum sample size required to be 95% confident that the sample standard deviation s, is within 5% of the true population standard deviationo. The population is normal. 12. Find the minimum sample size required to be 99% confident that the sample standard deviation s, is within 10% of the true population standard deviationo. The population is normal. 13. Find the minimum sample size required to be 99% confident that the sample standard deviation s, is within 1% of the true population standard deviationo. The population is normal