A school administrator is interested in a schools performance in math.  He administers a math test to a sample of 30 students and obtains a mean of 84.25.  The standard deviation of this sample was 8.4. (T Test)

26. Construct a 95% confidence interval for this data.

27. How would you interpret this confidence interval?

Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 9. The hypotheses H₀: μ = 75 and H_a: μ < 75 are to be tested using a random sample of n = 25 observations.

(a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.)
standard deviations

(b) If x = 72.3, what is the conclusion using α = 0.002?
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

State the conclusion in the problem context.

Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 75.Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 75.    Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 75.Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 75.

(c) For the test procedure with α = 0.002, what is β(70)? (Round your answer to four decimal places.)
β(70) =

(d) If the test procedure with α = 0.002 is used, what n is necessary to ensure that β(70) = 0.01? (Round your answer up to the next whole number.)
n =  specimens

(e) If a level 0.01 test is used with n = 100, what is the probability of a type I error when μ = 76? (Round your answer to four decimal places.)

2. (Binomial model) Consider a roulette wheel with 38 slots, of which 18 are red, 18 are black, and 2 are green (0 and 00). You spin the wheel 6 times.

(a) What is the probability that 2 of those times the ball ends up in a green slot? (

b) What is the probability that 4 of those times the ball ends up in a red slot?

3. (Normal approximation to binomial model) Take the roulette wheel from question 2. Assume that the wheel is spun 100 times, and you are interested in whether the ball ends up in a red slot.

(a) Verify that you can use the normal model here.

(b) Find the probability that the ball ends up in a red slot at least 60 times.

Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gains (+) or losses (−) in seconds per week.

3. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
4. Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the 0.01 significance level.
5. Estimate the p-value.

Bob is an amoeba that behaves as follows: at the end of any given minute, Bob either splits into two identical and independent copies of himself, stays the same without splitting, or dies; all three of these happen with equal probability. All subsequent Bobs behave identically and independently to the original Bob. If there is only 1 Bob at the start, find the expected number of Bobs after 2 minutes

This was the only information given in the question

In 2012, the Detroit Tigers and the San Francisco Giants met in baseball's World Series.  That year, the Tigers had a won-lost record of 88-74 and the Giants had a won-lost record of 94-68.   The question is whether the Giants were in fact the superior team based on their won-lost record.  So, test the claim that the 'true' proportion of their games won by the Giants was in fact higher than it was for the Tigers in 2012. Assume the only alternate hypothesis of interest is where the Giants are the superior team.   

The p-value of the hypothesis test is: ?????



Which of the following are correct conclusions?

At a 10% significance level, it would appear that the Giants were in fact the superior team.

At a 1% significance level, it would appear that the Giants were in fact the superior team.

At a 5% significance level, it would appear that the Giants were in fact the superior team.

At a 15% significance level, it would appear that the Giants were in fact the superior team.

It would seem that this 6-win difference over the course of the season is not statistically significant.

eBook Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

Dylan Jones kept careful records of the fuel efficiency of his new car. After the first twelve times he filled up the tank, he found the mean was 22.9 miles per gallon (mpg) with a sample standard deviation of 1.2 mpg.

1. Compute the 98% confidence interval for his mpg. (Use t Distribution Table.) (Round your answers to 3 decimal places.)

2. How many times should he fill his gas tank to obtain a margin of error below 0.15 mpg? (Use z Distribution Table.) (Round your answer to the next whole number.)

A study is performed in a large southern town to determine whether the average amount spent on fod per four person family in the town is significantly different from the national average. Assume the national average amount spent on food for a four- person family is $150.

A what is the null and alternative hypothesis?

b. Is the sample evidence significant? significance level?

A.) A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.9 years, and standard deviation of 1 years. If you randomly purchase one item, what is the probability it will last longer than 9 years?

B.) A particular fruit's weights are normally distributed, with a mean of 784 grams and a standard deviation of 24 grams. If you pick one fruit at random, what is the probability that it will weigh between 845 grams and 859 grams.

C.) A particular fruit's weights are normally distributed, with a mean of 615 grams and a standard deviation of 11 grams. The heaviest 19% of fruits weigh more than how many grams?
Give your answer to the nearest gram.

D.) A distribution of values is normal with a mean of 228.7 and a standard deviation of 33.7. Find P₈₅, which is the score separating the bottom 85% from the top 15%.
P₈₅ =

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

E.) The combined SAT scores for the students at a local high school are normally distributed with a mean of 1470 and a standard deviation of 303. The local college includes a minimum score of 2137 in its admission requirements.
What percentage of students from this school earn scores that satisfy the admission requirement?
P(X > 2137) = %
Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

7.16 How do you position yourself when you are going to sleep? A website tells us that 41% of use start in the fetal position, another 28% start on our side with legs straight, 13% start on their back, and 7% on their stomach. The remaining 11% have no standard starting sleep position. If a random sample of 1000 people produces the frequencies in the table below, should you doubt the proportions given in the article in the website? Show all the details of the test, and use a 5% significance level.

Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 67.1 grams and a standard deviation of 2.2 grams. a) For samples of size 12 pizza slices, what is the standard deviation for the sampling distribution of the sample mean? State answer to five decimal places. b) What is the probability of finding a random slice of pizza with a mass of less than 66.5 grams? State the answer to four decimal places. c) What is the probability of finding a 12 random slices of pizza with a mean mass of less than 66.5 grams? State the answer to four decimal places. d) What sample mean (for a sample of size 12) would represent the bottom 15% (the 15th percentile)? State answer to one decimal place. grams

A study conducted by Stanford researchers asked children in two elementary schools in San Jose, CA to keep track of how much television they watch per week. The sample consisted of 198 children. The mean time spent watching television per week in the sample was 15.41 hours with a standard deviation of 14.16 hours.

(a) Carry out a one-sample t-test to determine whether there is convincing evidence that average amount of television watching per week among San Jose elementary children exceeds fourteen hours per week. (Report the hypotheses, test statistic, p-value, and conclusion at the 0.10 level of significance.)

(b) Calculate and interpret a one-sample 90% t-confidence interval for the population mean.

(c) Comment on whether the technical conditions for the t-procedures are satisfied here. [Hint: What can you say based on the summary statistics provided about the likely shape of the population?]

2.In a test of the hypothesis H0: μ = 50 versus Ha: μ < 50, a sample of 40 observations is selected from a normal population and has a mean of 49.0 and a standard deviation of 4.1.

a) Find the P-value for this test.

b) Give all values of the level of significance α for which you would reject H0.

3.In a test of the hypothesis H0: μ = 10 versus Ha: μ≠ 10, a sample of 16 observations possessed mean 11.4 and standard deviation 3.1.

a) Find the P-value for this test.

b) Give all values of the level of significance α for which you would not reject H0.

What is a linear regression analysis? What does it provide you? Your answer should address development of a linear response equation and associated uncertainty in prediction.