Consider the value of t such that the area under the curve between −|t| and |t| equals 0.98.

Step 2 of 2:

Assuming the degrees of freedom equals 16, determine the t value. Round your answer to three decimal places.

Cesar wants to know what the expected weight of a loaf of bread for quality control purposes. Based on a sample of 14 loaves of bread, he finds a sample average of 400 grams with a sample standard deviation of 15 grams.

• What’s the confidence interval at 95%?  What is it at 99.9%?
• What would the confidence intervals (for 95% and 99.9%) be if the sample average was based on 140 loaves instead of 14?

When a truckload of apples arrives at a packing plant, a random sample of 150 apples are selected and examined for bruises and other defects. In reality, 12% of the apples on a particular truck are bruised or otherwise unsatisfactory. (a) How many standard errors away from 0.12 would you need to go to contain 89% of the sample proportions of bad apples you might expect to find? (3 decimal places) 1 (b) Suppose you were going to construct an 89% confidence interval from this population. What critical value should you use? (3 decimal places)

The polling organization Ipsos conducted telephone surveys in March of 2004, 2005 and 2006. In each year, 1001 people age 18 or older were asked about whether they planned to use a credit card to pay federal income taxes that year. The data are given in the accompanying table. Is there evidence that the proportion falling in the three credit card response categories is not the same for all three years? Test the relevant hypotheses using a .05 significance level. (Use 2 decimal places.) Intent to Pay Taxes with a Credit Card 2004 2005 2006 Definitely/Probably Will Might/Might Not/Probably Not Definitely Not 46 172 791 47 173 761 49 182 800 χ2 = P-value interval p < 0.001 0.001 ≤ p < 0.01 0.01 ≤ p < 0.05 0.05 ≤ p < 0.10 p ≥ 0.10

Three cards are chosen at random from a standard deck of 52.

1. What is the probability that all three cards are hearts?

2. What is the probability that all three cards are even?

3. What is the probability that all three cards are hearts and even?

4. What is the probability that all three cards are not aces?

e) What is the probability of at least one ace?

Recent evidence has surfaced regarding the effect of multiple CAT scans on the increase in risk for blood related cancers in children aged 5-18. Suppose after selecting 267 cases of childhood cancers, researchers found that 139 had received one or more CAT scans. Of the 382 matched sibling controls without blood cancers, only 89 reported having exposure to one or more CAT scan.

A) Calculate the risk difference between the groups for developing blood cancer based on exposure to one or more CAT scans versus never having received a CAT scan.

B) Construct a confidence interval about your point estimate for the difference in risk.

C) Carry out a formal statistical test to determine if there is a significant difference in risk between the groups.

Choose the most appropriate option

In a sample of 70 randomly selected students, 29 favored the amount being budgeted for next year's intramural and interscholastic sports. Construct a 98% confidence interval for the proportion of all students who support the proposed budget amount. (Give your answers correct to three decimal places.)

Are whites more likely to claim bias? A survey conducted by Barry Goldman Found that of 56 white workers terminated, 126 claimed bias. Of 407 black workers terminated, 126 claimed bias. a. Given that a worker is white, what then is the probability that the worker has claimed bias?

b. Given that a worker has claimed bias, what then is the probability that the worker is white?

c. Explain the difference in the results in (a) and (b).

d. Are the two events, “being white” and “claiming bias,” statistically independent? Explain

in an experiment on learning 70 rats were taught to navigate a maze during a 3 week training period. half the rats (n=35) were randomly selected to receive cocaine injections for a week while the other half received sodium placebos.

after the drug treatment the rats were then tested in the maze and their response times were recorded. for rats who received cocaine the sample mean was 16.83 seconds and ss= 903.04

for the rats who received the placebo the sample mean was 10.60 seconds and ss=380.46

a) what is the tables value of the t statistic at the .05 level

b) what is the calculated value of the t statistic

c) is the null hypothesis accepted or rejected at the .05 level

Foot Locker uses sales per square foot as a measure of store productivity. Last year, the mean annual sales per square foot was $390 with a standard deviation of $45.83. Suppose you take a random sample of 49 Foot Locker stores operating last year. There is a 16% probability that the sample mean annual sales per square foot is at most $______.

Thirty-one small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 43.7 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 7 6 12 14 a. Using the following equation: 12.32a.jpg Estimate the standard deviation of ŷ* when x = 3. b. Using the following expression: 12.32b.jpg Develop a 95% confidence interval for the expected value of y when x = 3. c. Using the following equation: 12.32c.jpg Estimate the standard deviation of an individual value of y when x = 3. d. Using the following expression: 12.32d.jpg Develop a 95% prediction interval for y when x = 3.

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 44 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.92 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.43 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
  farming regions ?

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)

A system consisting of two components is subject to a series of shocks that arrive according to a Poisson process with a rate of one per day. Half the shocks cause no damage, one in ten damages component 1 alone, one in five damages component 2 alone, and the rest damage both components. Note that if only one component is functioning, and a shock occurs that would damage both components, the functioning component is damaged. Compute the probability that the at least one component is still functioning after 5 days.