the midpoint of a class is the sum of its lower and upper limits divided by two

Using the data found in Table 4 and Bayes’ Formula, determine the probability that a randomly selected patient will have Strep Throat given the SARTD test result was positive. Use the CDC stated prevalence of 25%. Round answer to nearest hundredth of a percent (i.e. 45.67%).

Then using the same Table 4, and Bayes’ Formula, determine the probability that a randomly selected patient will not have Strep Throat given the SARTD test result was negative. Use the CDC stated prevalence of 25%. Round answer to nearest hundredth of a percent.

Many people grab a granola bar for breakfast or for a snack to make it through the afternoon slump at work. A Kashi GoLean Crisp Chocolate Caramel bar weights 45 grams. The mean amount of protein in each bar is 8 grams. Suppose the distribution of protein in a bar is normally distributed with a standard deviation of 0.27 grams and a random Kashi bar is selected.

c) Find a symmetric interval about the mean such that 98.64% of all amounts of protein lie in this interval.
d) Suppose the amount of protein is at least 8.1 grams. What is the probability that it is more than 8.3 grams?

Professor Fair believes that extra time does not improve grades on exams. He randomly divided a group of 300 students into two groups and gave them all the same test. One group had exactly 1 hour in which to finish the test, and the other group could stay as long as desired. The results are shown in the following table. Test at the 0.01 level of significance that time to complete a test and test results are independent.

(i) Give the value of the level of significance.


State the null and alternate hypotheses.

H₀: The distributions for a timed test and an unlimited test are the same.
H₁: The distributions for a timed test and an unlimited test are different.H₀: Time to take a test and test score are not independent.
H₁: Time to take a test and test score are independent.    H₀: Time to take a test and test score are independent.
H₁: Time to take a test and test score are not independent.H₀: The distributions for a timed test and an unlimited test are different.
H₁: The distributions for a timed test and an unlimited test are the same.

(ii) Find the sample test statistic. (Round your answer to two decimal places.)


(iii) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(iv) Conclude the test.

Since the P-value < α, we reject the null hypothesis.Since the P-value is ≥ α, we do not reject the null hypothesis.    Since the P-value < α, we do not reject the null hypothesis.Since the P-value ≥ α, we reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.

At the 1% level of significance, there is insufficient evidence to claim that time to do a test and test results are not independent.At the 1% level of significance, there is sufficient evidence to claim that time to do a test and test results are not independent.    

Condé Nast Traveler conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a 100-point scale, with higher values indicating better service. A sample of 36 ships that carry fewer than 500 passengers resulted in an average rating of 85.33 , and a sample of 43 ships that carry 500 or more passengers provided an average rating of 81.3. Assume that the population standard deviation is 4.55 for ships that carry fewer than 500 passengers and 3.95 for ships that carry 500 or more passengers.

A.) What is the point estimate of the difference between the population mean rating for ships that carry fewer than 500 passengers and the population mean rating for ships that carry 500 or more passengers?

B.) At 95% confidence, what is the margin of error?

C.) What is a 95% confidence interval estimate of the difference between the population mean ratings for the two sizes of ships?

[ ] to [ ]

Describe the connection between a correlation and a bivariate regression analysis. In your discussion, specifically note: 1) statistical significance, 2) sign, and 3) use or application.

A researcher thinks that listening to classical music reduces anxiety. She measures the anxiety of 10 persons then plays Mozart's "Eine Kleine Nachtmusik". Following that the researcher measures their anxiety again. (Note that anxiety is measured on a scale from 1 to 7, with higher numbers indicating increased anxiety.)

Does the study support her hypothesis? Compute the upper bound of the confidence interval using the following data:

mean of the difference scores (subtract pretest from posttest): -1.6

standard error of the difference scores: 0.4

The formula for the CI upper bound is [standard error of the difference scores]*[t critical value]+[mean of the difference scores]

How do you find the t critical value? and what is the value for the upper bound?

Consider the following results for two independent random samples taken from two populations.

Sample 1:

n1 = 40

x̅1 = 13.9

σ1 = 2.3

Sample 2:

n2 = 30

x̅2 = 11.1

σ2 = 3.4

What is the point estimate of the difference between the two population means? (to 1 decimal)

Provide a 90% confidence interval for the difference between the two population means (to 2 decimals).

Provide a 95% confidence interval for the difference between the two population means (to 2 decimals).

Suppose X and Y are independent random variables with X = 2:8 and Y = 3:7. Find X+Y , the standard deviation of X + Y .

Department of Labor reported the average hourly earnings for production workers to be $15.23 per hour in 2001. A sample of 75 production workers during 2003 showed a sample mean of $15.86 per hour. Assuming the population standard deviation is $1.50, can we conclude that an increase occurred in the mean hourly earnings since 2001? Use α = .05

a sample size n =44 has sample mean =56.9 and Sample standard deviation s =9.1. a. construct a 98% confidence interval for the population mean meu b. if the sample size were n =30 would the confidence interval be narrower or wider? please show work to explain

1. Explain the difference between non-directional and directional hypotheses, and explain in which circumstances it is important to apply directional hypothesis.
2. Explain why Chi square distributions are positively skewed and what is its relationship with the degrees of freedom.
3. The objective of hypothesis testing is to reject the null hypothesis. How do we use the P-value to accomplish this goal?
4. Describe the difference between One-way versus Two-way ANOVA and provide an example of each.

1, You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion, so we assume p=.5. You would like to be 99% confident that you esimate is within 4% of the true population proportion. How large of a sample size is required?
n =

Hint: Shouldn't the answer be a WHOLE NUMBER.
Do not round mid-calculation. However, use a critical value accurate to three decimal places.

2. You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 84%. You would like to be 98% confident that your estimate is within 3.5% of the true population proportion. How large of a sample size is required?

n =

3. A political candidate has asked you to conduct a poll to determine what percentage of people support her, assume p=.5.
If the candidate only wants a 2% margin of error at a 99% confidence level, what size of sample is needed?

4. If n = 540 and ˆp (p-hat) = 0.35, construct a 99% confidence interval.

Give your answers to three decimals

< p <

Dr. Smile is interested in evaluating whether 7-year-old autistic children differ from the general population of 7-year-old children in their ability to recognize facial expressions. She develops the Facial Recognition Test, which has mean = 200 among the general population of 7-year-olds. Dr. Smile collects data on a sample of 16 children with autism. In this sample Xbar = 180 and s = 12.

A) using alpha= 0.05 and a two-tailed test, conduct a one-sample t-test evaluating the null hypothesis.

b) based on these results, should Dr Smile reject or fail to reject the null hypothesis?

c)Report the resukts of the hypothesis test you conducted in part B as if Dr Smile were writing about them in a journal article.