Exponential distribution with λ = 0.5 Apply Chi-Square test to see whether the your hypothesized distribution fits your data. using excel

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of medical files is used to estimate the proportion p of all people who have blood type B.

(a) If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate p̂ will be within a distance of 0.04 from p? (Round your answer up to the nearest whole number.)
medical files

(b) Answer part (a) if you use the preliminary estimate that about 12 out of 90 people have blood type B.
medical files

Suppose that in a certain region of California, earthquakes occur at the average rate of 7 per year.

(a) What is the probability that in exactly three of the next eight years, no earthquakes occur?

(b) What is the **expect**ed number of years to wait until we have a year with exactly 7 earthquakes?

(c) In the next century, how many years would you **expect** to see with more than 10 earthquakes?

Hint: When you see the word "expect" you should expect to use the expected value!

30 students were randomly selected from a large group of students taking a certain test. The mean score for the students in the sample was 86.
Assume that σ = 11.1. Construct a 99% confidence interval for the mean score, μ, of all students

Suppose a survey revealed that 22% of 502 respondents said they had in the past sold unwanted gifts over the Internet.

(a) Use the information to construct a 90% confidence interval for the population proportion who sold unwanted gifts over the Internet, rounding your margin of error to the nearest hundredth. (Round your answers to two decimal places.)
(  ,  )

(b) Use the information to construct a 98% confidence interval for the population proportion who sold unwanted gifts over the Internet, rounding your margin of error to the nearest hundredth. (Round your answers to two decimal places.)
(  ,  )
(c) Which interval has a higher probability of containing the true population proportion?

the 90% confidence interval

the 98% confidence interval    

(d) Which interval is narrower?

the 90% confidence interval

the 98% confidence interval  

Scholastic Aptitude Test (SAT) mathematics scores of a random sample of 100 high school seniors in the state of Texas are collected, and the sample mean and standard deviation are found to be 520 and 80, respectively. Find a 95% confidence interval on the mean SAT mathematics score for seniors in the state of Texas.

A community health association is interested in estimating the average number of maternity days women stay in the local hospital. A random sample is taken of 36 women who had babies in the hospital during the past year. The following numbers of maternity days each woman was in the hospital are rounded to the nearest day. 3 3 4 3 2 5 3 1 4 3 4 2 3 5 3 2 4 3 2 2 1 6 3 4 3 3 5 2 3 3 3 5 4 3 5 4 Use these data and a population standard deviation of 1.12 to construct a 98% confidence interval to estimate the average maternity stay in the hospital for all women who have babies in this hospital.

Listed below is the population by state for the 15 states with the largest population. Also included is whether that state's border touches the Gulf of Mexico, the Atlantic Ocean, or the Pacific Ocean (coastline).

Suppose three states are selected at random. Calculate the probability for the following:

1. None of the states selected have a population of more than 9,000,000. (Round your answer to 3 decimal places.)

2. Exactly one of the selected states has a population of more than 9000000 (Round your answer to 3 decimal places.)

3. At least one of the selected states has a population of more than 9000000 (Round your answer to 3 decimal places.)

Suppose the following data are selected randomly from a population of normally distributed values. 41 51 43 48 44 57 54 39 40 48 45 39 40 Construct a 95% confidence interval to estimate the population mean.

Every few years, the National Assessment of Educational Progress asks a national sample of eighth-graders to perform the same math tasks. The goal is to get an honest picture of progress in math. Suppose these are the last few national mean scores, on a scale of 0 to 500

. Year 1990 1992 1996 2000 2003 2005 2008 2011 2013

Score 263 266 272 273 277 278 280 286 288

(a) Make a time plot of the mean scores, by hand. This is just a scatterplot of score against year. There is a slow linear increasing trend.

(b) Find the regression line of mean score on time step-by-step. First calculate the mean and standard deviation of each variable and their correlation (use a calculator with these functions). Then find the equation of the least-squares line from these. (Round your answers to two decimal places.)
ŷ =   +   x

Draw the line on your scatterplot. What percent of the year-to-year variation in scores is explained by the linear trend? (Round your answer to one decimal place.)
  %

2. A recent poll revealed that 54 out of 96 people believed honeydew should be removed from all versions of fruit salad. Create a 92% confidence interval and discuss whether or not this data reflects the belief most people would wish to remove honeydew from fruit salad. Make sure to use your confidence interval in your explanation.

4. A recent poll found 48 out of 92 professors would be willing to add 30 minutes to every class schedule to lower their amount of office hours. Of the students who were polled, only 30 of the 63 of them believed adding time to the class schedule in lieu of office hours was a good idea. Create a 95% confidence interval to see if the perspective of the professors is different from the students.

The times that college students spend studying per week have a distribution skewed to the right with a mean of 7.6 hours and a standard deviation of 2.6 hours. Find the probability that the mean time spent studying per week for a random sample of 45 college students would be

a. between 7.0 and 7.9 hours.

Round your answer to two decimal places.

P=____

b. less than 7.3 hours.

Round your answer to two decimal places.

P=____

Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 112.
(a)  If 1 man is randomly selected, find the probability that his score is at least 585.

(b)  If 16 men are randomly selected, find the probability that their mean score is at least 585.

16 randomly selected men were given a review course before taking the SAT test. If their mean score is 585, is there strong evidence to support the claim that the course is actually effective?
(Enter YES or NO)  

A group of chemists wanted to determine whether a new catalyst 2 increased the reaction rate of a particular chemical reaction relative to that same chemical reaction with an older catalyst 1. The duration of the reactions, in seconds, are recorded below:

Catalyst 1: 14.1,18.9,22,21.2,25.3,16.8,18.7,15.3,20.4,16.6,19.5,12.9,20.6,17.2,20.4

Catalyst 2: 18.2,16.7,16.5,17.6,15.8,15.3,17.2,16,17.4,16.9

(a) Plot the data using side-by-side box plots in R.

(b) Check the assumptions for performing a two-sample t-test.

(c) Perform the appropriate two sample t test for means at the 5% level. As part of this test, specify your hypotheses, calculate a p value and make a conclusion in the context of the question. Compute the results by hand and then again using the t.test function in R.

(d) Construct and interpret a 95% confidence interval for the true difference in means (by hand and then again in R) applying the same assumptions as in part c. Describe how this confidence interval relates to your findings in part c.

An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. Suppose that the mean income is found to be $36.6 for a random sample of 1012 people. Assume the population standard deviation is known to be $8.5. Construct the 80% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.