HW: Section 5.1 & 5.3

Three confidence intervals for a population mean are constructed, all from the same random sample. The confidence levels are 95%, 98%, and 99.9%. The confidence intervals are (6.1, 12.4), (5.4, 13.7), and (6.7, 11.7). Match each confidence interval to its level. (6.7, 11.7) (5.4, 13.7) (6.1, 12.4)

(6.7, 11.7) confidence level 95% (5.4, 13.7) confidence level 99.9% (6.1, 12.4) confidence level 98%

A 95% confidence interval for a population mean is computed from a sample of size 400. Another 95% confidence interval will be computed from a sample of size 100 drawn from the same population. Choose the best answer to fill in the blank: The interval from the sample of size 400 will be approximately _____ as the interval from the sample of size 100.

sqrt(100)/sqrt(400) = 1/2 One-half as wide

Sixty-four independent measurements were made of the speed of light. They averaged 299,795 km/s and had a standard deviation of 8 km/s. A 95% confidence interval for the speed of light is 299,795 ± 1.96 km/s.

mean +- critical value of 0.05 (95%) is 1.96 True

A sample of 114 patients were given a drug to lower cholesterol. A 95% confidence interval for the mean reduction in cholesterol (in mmol/L) was (0.93, 1.05). What was the sample mean reduction? (Round the final answer to two decimal places.) The sample mean reduction was _________mmol/L.

0.99

Find the value of tn-1,α needed to construct a 90% upper or lower confidence bound with sample size 12. Round the answer to three decimal places.

1.796?

Find the value of zα/2 to construct a confidence interval with level 95%. Round the answer to two decimal places.

1.96

Fission tracks are trails found in uranium-bearing minerals, left by fragments released during fission events. An article reports that fifteen tracks on one rock specimen had an average track length of 11 μm with a standard deviation of 2 μm. Assuming this to be a random sample from an approximately normal population, find a 99% confidence interval for the mean track length for this rock specimen. Round the answers to three decimal places. The 99% confidence interval is ( _____,_______ ).

11 +- 2.977 [2 / sqrt(15) ] 9.463 , 12.537

The sugar content in a one-cup serving of a certain breakfast cereal was measured for a sample of 140 servings. The average was 11.9 g and the standard deviation was 1.1 g. Find a 95% confidence interval for the mean sugar content. Round the answers to three decimal places. The 95% confidence interval is (______ ,_______ ).

11.9 +- 1.96 [ 1.1/sqrt(140)] 11.718 , 12.082

An article presents a new method for timing traffic signals in heavily traveled intersections. The effectiveness of the new method was evaluated in a simulation study. In 50 simulations, the mean improvement in traffic flow in a particular intersection was 652.3 vehicles per hour, with a standard deviation of 311.7 vehicles per hour. Find a 95% confidence interval for the improvement in traffic flow due to the new system. Round the answers to three decimal places. The 95% confidence interval is (________ ,________ ).

652.3 +- 1.96 [311.7/sqrt(50)] 565.901 , 738.699

In a sample of 100 steel canisters, the mean wall thickness was 8.1 mm with a standard deviation of 0.7 mm. Find a 95% lower confidence bound for the mean wall thickness. (Round the final answer to three decimal places.) The 95% lower confidence bound is

8.1 - 1.6604 [ 0.7 / sqrt(100) ] 7.984

Find the level of a two-sided confidence interval for t = 2.776 with sample size 5. Express the answer as a percent.

95%

Find the level of the confidence interval that has the value zα/2zα/2 = 1.96. Express the answer as a percent and round to the nearest integer.

95%

A sample of 114 patients were given a drug to lower cholesterol. A 95% confidence interval for the mean reduction in cholesterol (in mmol/L) was (0.93, 1.05). What was the sample standard deviation of the reduction amounts? The standard deviation was ___________ mmol/L.

E= upperCL-lowerCL/2 t critical value is 1.981 E=t*s/sqrt(n) 0.07x10.677/1.981 = s 0.32

The Student's t distribution may be used to construct a confidence interval for the mean of any population, so long as the sample size is small.

If population has outliers or strong asymmetry then cannot use t distribution. False

As the confidence level goes up, the reliability goes _____________ up down and the precision goes __________

up down