STAT1401 EXAM 4 STUDY GUIDE

(a) A sample of size n = 35 is drawn from a population whose standard deviation is σ = 19. Find the margin of error for a 95% confidence interval for μ. Round the answer to at least three decimal places. (b) If the sample size were n = 61, would the margin of error be larger or smaller?

(a) Remember that the Margin of Error is found by multiplying the critical value times the standard error. First, find the critical value the same way you did for Problem #2 on the test. To find the standard error use the formula σ / the square root of n Multiply the standard error by the critical value - the answer for this specific problem should be 6.295. (b) The margin of error would be smaller if the sample size were to be larger.

In a sample of 43 water specimens taken from a construction site, 23 contained detectable levels of lead.

Use 1PropZInt for this problem as well

A sample of size n = 48 has sample mean x = 54.6 and sample standard deviation s = 9.2 (a) Construct a 99.9% confidence interval for the population mean μ. Round the answers to one decimal place (b) If the sample size were n = 41, would the confidence interval be narrower or wider?

(a) Use the TInterval function on the calculator (under STAT, TESTS) Input the mean, standard deviation, sample size n, and confidence level as a decimal Answer should be 49.9 < μ <59.3 (b) wider, because the sample size is smaller

A sample of size n = 86 is drawn from a normal population whose standard deviation is σ = 6.3. The sample mean is x̅ = 40.52. (a) Construct a 99.8% confidence interval for μ. Round the answer to at least two decimal places. (b) If the population were not approximately normal, would the confidence interval constructed in part a be valid? Explain.

(a) Use the ZInterval function on the calculator (under STAT, TESTS) Enter the standard deviation, mean, sample size n, and the confidence level (c-level) as a decimal (.998 rather than 998) (b) The confidence interval constructed in part (a) would be valid since the sample size is large.

For the given confidence level and values of x and n, find the following. x = 47, n = 98, confidence level 90% (a) point estimate (b) standard error (c) margin of error

(a) point estimate is x/n (b) standard error is found using a different formula this time since we are given different information the square root of the point estimate times 1 − the point estimate divided by n (c) standard error times the critical value

Use the given data to construct a 99% confidence interval for the population proportion p. x = 49 n = 68

Use 1PropZInt function on the calculator

A simple random sample of 100 U.S. college students had a mean age of 23.04 years. Assume the population standard deviation is σ = 4.79 years. Construct an 80% confidence interval for the mean age of U.S. college students. Round the answers to two decimal places.

Use the ZInterval function

To estimate the necessary sample size when no value of is available, we use p =

0.5

Find the critical value z/α2 needed to construct a confidence interval with level 80%.

Use the Calculator: The confidence level is 80% Therefore, 1 minus (-) .80 = 0.2 0.2 divided by (/) 2 = 0.1 1 minus (-) 0.1 = 0.9 Go to the invNorm function under 2nd VARS input 0.9 for the area and make sure μ = 0 and σ = 1 Round the answer to two decimal places (in this case it would be 1.28)

For determining the type of alternate hypothesis

> = right-tailed < = left-tailed ≠ = two-tailed

The National Health Statistics Reports described a study in which a sample of 345 one-year-old baby boys were weighed. Their mean weight was 25.7 pounds with standard deviation 5.3 pounds. A pediatrician claims that the mean weight of one-year-old boys is greater than 25 pounds. Do the data provide convincing evidence that the pediatrician's claim is true? Use the α =0.05 level of significance

A pediatrician claims that the mean weight of one-year-old boys is greater than 25 pounds. Greater than = this will be right-tailed Use the T Test Function in the calculator

A community survey sampled 1923 people in Colorado and asked them how long it took them to commute to work each day. The sample mean one-way commute time was 24.1 minutes with a standard deviation of 13 minutes. A transportation engineer claims that the mean commute time is less than 25 minutes. Do the data provide convincing evidence that the engineer's claim is true? Use the=α0.10 level of significance

A transportation engineer claims that the mean commute time is less than 25 minutes. Less than = this will be left-tailed Use the T TestFunction in the calculator

Making sure that the scales used by businesses in the United States are accurate is the responsibility of the National Institute for Standards and Technology (NIST) in Washington, D.C. Suppose that NIST technicians are testing a scale by using a weight known to weigh exactly 1000 grams. The standard deviation for scale reading is known to be σ = 2.0. They weigh this weight on the scale 55 times and read the result each time. The 55 scale readings have a sample mean of x̅ = 1000.6 grams. The scale is out of calibration if the mean scale reading differs from 1000 grams. The technicians want to perform a hypothesis test to determine whether the scale is out of calibration. Use the α = 0.10 level of significance and the P-value method with the TI-84 calculator.

Since they are testing whether it differs, it's going to be a two-tailed test Use the Z Test function in the calculator (STAT, TESTS)

Rejecting the null hypothesis when it is true is a _______________

Type I Error

Find the critical value t/α2 needed to construct a confidence interval of the given level with the given sample size. Round the answers to three decimal places. For level 80% and sample size 6

Use the invT function on the calculator under 2nd VARS Find the critical value using the confidence level and enter that in for area the "df" will be n - 1 (so for this problem it would be 5 instead of the sample size given, 6) Answer should be 1.476

Rejecting the null hypothesis when it is false is a ______________

correct decision

If we increase the confidence level and keep the sample size the same, we _________ the margin of error.

increase

In the confidence interval 24.31.2, the quantity 1.2 is called the

margin of error

(a) How large a sample must be drawn so that a 99% confidence interval for μ will have a margin of error equal to 4.4? Round the critical value to no less than three decimal places. Round the sample size up to the nearest integer. (b) If the required confidence level were 95%, would the necessary sample size be larger or smaller?

n = (z a/2 times σ) / margin of error to the 2nd power The answer for this particular problem is 102 (b) Smaller, because the confidence level is lower .

When the number of degrees of freedom is large, the Student's t distribution is close to the __________________ distribution.

normal

The smaller the P-value is, the stronger the evidence against the _______________ becomes.

null hypothesis

When results are statistically significant, they do not necessarily have __________significance.

practical

The number of degrees of freedom for the Student's t-test of a population mean is always 1 less than the ___________________

sample size

State which type of parameter is to be estimated, and the correct method for the following. Do not solve.

the parameter is what they want to solve for it's z if they use σ for the standard deviation. If they use s as standard deviation, it's t UNLESS they say the population is normally distributed (NOT approximately normally distributed), then it's chi-square