A researcher conducts a study on the effects of amount of sleep on creativity. Twenty subjects come to the researcher’s clinic. The researcher divides the subjects into four groups, each containing five subjects. Each group sleeps at the clinic for a different amount of time (2, 4, 6, or 8 hours). After awakening, each subject takes a test of creativity. The following table shows the creativity scores for the subjects in each group:

1. State the appropriate null and alternative hypotheses
2. Fill in the blanks in the following summary (source) table describing the results of the ANOVA:

3. Find the critical value of F. Assume a level of significance of .05.
4. Based on the results of the ANOVA, what is the correct conclusion regarding the null hypothesis?
5. What does this result mean in terms of the alternative hypothesis?
6. Should you perform a post hoc test in this case? Explain why or why not. What information does the post hoc test provide?
7. Conduct a Tukey’s HSD test to test the differences between all possible pairs of sample means at the .05 level of significance and complete the following table.

8. What is the value of Q_CRIT?
9. Which pairs of sample means are significantly different?

INCLUDE:

all Hypothesis Tests must include all four steps, clearly labeled

all Confidence Intervals must include all output as well as the CI itself

include which calculator function you used for each problem

At a community college, the mathematics department has been experimenting with four different delivery mechanisms for content in their Statistics courses. One method is traditional lecture (Method I), the second is a hybrid format in which half the time is spent online and half is spent in-class (Method II), the third is online (Method III), and the fourth is an emporium model from which students obtain their lectures and do their work in a lab with an instructor available for assistance (Method IV). To assess the effective of the four methods, students in each approach are given a final exam with the results shown in the following table. Assume an approximate normal distribution for each method. At the 5% significance level, does the data suggest that any method has a different mean score from the others?

Method I: 81, 81, 85, 67, 88, 72, 80, 63, 62, 92, 82, 49, 69, 66, 74, 80

Method II: 85, 53, 80, 75, 64, 39, 60, 61, 83, 66, 75, 66, 90, 93

Method III: 81, 59, 70, 70, 64, 78, 75, 80, 52, 45, 87, 85, 79

Method IV: 86, 90, 81, 61, 84, 72, 56, 68, 82, 98, 79, 74, 82,

(be very careful when inputting your data; triple check, if necessary)

Some sources report that the weights of full-term newborn babies have a mean of 7 pounds and a standard deviation of 0.6 pound and are Normally distributed. What is the probability that one randomly selected newborn baby will have a weight over 8 pounds? What is the probability the average of four babies' weights will be over 8 pounds? Explain the difference between parts 1 and 2.

Include:

all hypothesis tests with all four steps

all Confidence Intervals with all output as well as the CI itself'

all calculator functions used

An experiment was done to see whether open-book tests make a difference. A calculus class of 48 students agreed to be randomly assigned by the draw of cards to take a quiz either by open-notes or closed-notes. The quiz consisted of 30 integration problems of varying difficulty. Students were to do as many as possible in 30 minutes. The 24 students taking the exam closed-notes got an average of 15 problems correct with a standard deviation of 2.5. The open-notes crowd got an average of 12.5 correct with a standard deviation of 3.5. Assume that the populations are approximately normal. At the 5% significance level, does this data suggest that differences exist in the mean scores between the two methods?

1. Construct an 80​% confidence interval to estimate the population mean when x overbarx=128 and s​ =27 for the sample sizes below.​

a)n=20       

​b)n=50       

​c)n=90

​a) The 80​% confidence interval for the population mean when n=20 is from a lower limit of ____ to an upper limit of _____. (Round to two decimal places as​ needed.)

_______________________________________________________________________

2. Determine the margin of error for a confidence interval to estimate the population mean with n=25 and s-12.5 for the following confidence levels:

a. 80% b. 90% c.99%

In a study to evaluate drug efficacy, the manufacturer of a new type of generic drug for treating a
disease wants to investigate the effectiveness of this generic drug as compared to the traditional
brand name drug, At the present time, the brand name drug is the only approved treatment for the
disease. Patients diagnosed with the disease have low concentration of a specific factor in their
blood. Treatment with the brand name drug will result in an increase in the concentration of the
specific factor in the blood. An experiment is conducted in which 10 patients currently with the
disease are randomly assigned to receive either the generic drug or the brand name drug for a
period of 9 months. After 9 months have elapsed, a measure of the concentration level of the
specific factor in the blood is obtained for each patient. The results are shown in Table Q1.

(a) At a 5 % level of significance, apply a two-sample t test to determine whether there is
any difference in the concentration levels between brand name drug and generic drug.
Comment on the results.

(b) Construct a 90 % confidence interval for the difference in the mean concentration
levels between brand name drug and generic drug.

(c) Suppose now the manufacturer wishes to demonstrate whether the concentration level
of brand name drug exceeds that of generic drug by more than 1, apply a two-sample t
test to analyze the problem based on 1 % level of significance.

Please show workings and do not use excel to generate answer.

A component of cholesterol called high-density lipoprotein is known to lower the risk of coronary heart disease. It is believed that runners have increased HDL levels. The following data give details of an HDL study comparing male elite runners with a control group of male nonrunners. At the α=0.05, test the claim that young male elite runners have a higher population mean HDL level than young male nonrunners.

Consider the following equation:

^CHICKEN = -85.4 - 0.58 PRICE + 88.76 ln (YD)

CHICKEN - per capita consumption of chicken in pounds

PRICE - price of chicken in dollars per pound

YD - disposable income

a) Interpret the coefficient of ln(YD)

Let n₁=40 , p₁=0.60 and n₂=50 and p₂=0.40.

Given: H0:π1≤π2{"version":"1.1","math":"H_0: \pi_1 \leq \pi_2"}

Calculate the test statistic and p-value.

(a)-0.0261 and 0.4896 (b)1.8861 and 0.0296 (c) -0.9428 and 0.1729 (d) -0.4714 and 0.3939

1. Identify the correct statements. Fix the incorrect ones.

   1. A sampling distribution describes the distribution of data values.

   2. A sampling distribution shows the behavior of a sampling process over many samples.

   3. The probability distribution of a parameter is called a sampling distribution.

   4. Sampling distributions describe the values of a data summary for many samples.

At a local coffee house, 80% of coffee buyers will choose regular coffee, and
20% will choose decaf.
A. Out of the next 5 customers, what is the probability that 3 will choose decaf coffee?
B. Out of the next 20 customers, what is the probability that at least 10 will choose decaf
coffee?

1. Let Z be a standard normal random variable. Find…

a. Pr (Z ≥ -0.78) b. Pr(-0.82  Z  1.31)

2. A random variable X is normally distributed with mean ? = 25.5 and standard deviation ? .0= 3.25.

Find Pr(23.03 ≤ ?? ≤ 29.14)

3. The math SAT is scaled so that the mean score is 500 and the standard deviation is 100.
Assuming scores are normally distributed, find the probability that a randomly selected student
scores

a. higher than 645 on the test. b. at most 475 on the test   

4. Adult male heights are a normal random variable with mean 69 inches and a standard deviation of 3 inches. Find the height, to the nearest inch, for which only 8 percent of adult males are taller (i.e. find the 92nd percentile)