Statistics and Probability Answers

For the confidence interval below, what is the sample mean, ?

Find the t value such that the area to the left of –t equals 0.1. Assume 25 degrees of freedom.

In a random sample of 12 residents of Benton the mean waste recycled per person was 1.3 pound with a standard deviation of 0.25 pounds. What is the 80% confidence interval for the mean waste recycled per person?

From a sample of 10 squirrels the average weight was 511 grams with standard deviation of 160 grams.

What is the t value for a 95% confidence interval?


What are the lower and upper limits of the 95% confidence interval?

Landoldt et al. (J Child Psychol Psychiat. 44:1199-1207) examined rates of posttraumatic stress disorders (PTSD) in mothers and fathers. Parents were interviewed 5 to 6 weeks after an accident or a new diagnosis of cancer or diabetes mellitus for their child. The 2003 survey found that 28 of the 175 fathers interviewed and 43 of the 180 mothers interviewed met the criteria for current PTSD.
a. What is p-hat, the weighted average of the proportion?
b. What is the null hypothesis if comparing mothers to fathers?
c. What is the p-value of the two-sided test?
d. At the 0.05 level of significance, can we conclude that fathers and mothers are not equally likely to develop PTSD after stress?

In a 2003 article, Hui and Bell (Health and Place. 9:371-376) reported that among 2,428 boys aged 7 to 12 years, 461 were overweight or obese.
a. On the basis of that study, can we conclude that more than 15 percent of the boys aged 7 to 12 in the sampled population are overweight?
b. What is the p-value?
c. What was the null hypothesis?

9.23: Suppose that a random sample of nine measurements from a normally distributed population gives a sample mean of _ = 2.57 and a sample standard deviation of s = .3. Use critical values to test H0 : μ = 3 versus Ha : μ ≠3 using levels of significance α = .10, α = .05, α = .01, and α = .001.

9.19: The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, μ, is close to the target fill of 16 ounces. To this end, a random sample of 36 filled bottles is selected from the output of a test filler run. If the sample results cast a substantial amount of doubt on the hypothesis that the mean bottle fill is the desired 16 ounces, then the filler’s initial setup will be readjusted.

a: The bottling company wants to set up a hypothesis test so that the filler will be readjusted if the null hypothesis is rejected. Set up the null and alternative hypotheses for this hypothesis test.

9.9: Explain what a p-value is, and explain how it is used to test a hypothesis.

9.8: Explain what a critical value is, and explain how it is used to test a hypothesis.