Unit 1 Lesson 3: Standard Deviation Is Not Known

The mean of a sample size n = 35 is 1860. The standard deviation of the sample is 102 and the population is normally distributed. Construct a 99% confidence interval estimate of the mean of the population

1813 < u < 1907

A simple random sample has a sample size of n = 65. Given the population is normally distributed, find the critical value t a/2 corresponding to a 99% confidence level

2.660

Assume you want to construct a 98% confidence interval with a sample of n = 10 from of a normally distributed population. Find the critical value t a/2

2.821

Assume a random sample of the birth weights of 186 healthy babies has a mean of 3103 g and a st. dev. of 696 g. Construct a 95% confidence interval estimate of the mean weight of all healthy babies born to healthy mothers. What does the interval suggest about a recent study informing soon-to-be parents that they can expect their new baby to weigh about 2980 g

3002 g < u < 3204 g; the 2980 g weight falls below the interval, suggesting that is is unlikely to be an expected value and is likely too low to represent an accurate population mean

You are constructing a 90% confidence interval for a sample consisting of n = 9 values and an unknown population st. dev. The population appears to be very skewed. Determine whether a margin of error should be calculated using a critical value of z a/2, a critical value of t a/2, or neither

neither

In a test for the effectiveness of garlic for lowering cholesterol, 47 subjects were treated with garlic in tablet form and the changes in LDL cholesterol measured in mg/dL were recorded. The mean of the sample group is 3.2 with a st. dev. of 18.6. Construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval level suggest about the effectiveness of garlic in reducing LDL cholesterol?

-2.3 < u < 8.7; the interval contains 0, which suggests that garlic could easily have no effect on the cholesterol

To determine the weight of plastic discarded by households, a sample size of 62 weights are measured and are found to have a mean of 1.911 and a st. dev. of 1.065 lb. Construct a 99% confidence interval estimate of the mean weight of plastic discarded by all households

1.551 lb < u < 2.271 lb

Assume you want to construct a 90% confidence interval from sample of a normally distributed population. The sample size is 37. Find the critical value t a/2

1.688

A sample of 20 silver dollar coins is weighed. The mean of the sample is 8.0710 g and the st. dev. of the sample is 0.0411 g. Construct a 95% confidence interval estimate of the mean weight of all the coins

8.0518 g < u < 9.0902 g

You are constructing a 95% confidence interval of a sample space consisting of n = 40 values and a population st. dev. of 2.6. The population appears to be skewed. Determine whether a margin of error should be calculated using a critical value of z a/2, a critical value of t a/2, or neither

A critical value of z a/2