1. A variable is normally distributed in the population with a mean of 100 and a standard deviation of 10. A sample of 20 is randomly selected. The probability that the sample mean is between 90 and 110 is _______ the probability that the variable is between 90 and 110.

1. Conduct a one way between subjects’ ANOVA using SPSS

Students were randomly assigned to attend an ANOVA lecture that contains one of the following approaches to instructions. 1) Mathematical, 2) Conceptual, 3) Conceptual and Mathematical. After the lecture, each student took an ANOVA exam. The table below displays the scores by condition for each student. Are there any significant differences between the groups?

a. State the null hypothesis.

b.State the alternative hypothesis.

c.Provide the SPSS output for the test identify (circle or highlight) the F-obtained and the p-value. Provide full calculations for the results and explain how did you do it.

d.Did you reject or fail to reject the null hypothesis?

e.Explain the results in terms of which groups are significantly different from which. Provide full explanation, calculations and reason for doing those calculations.

Thank you

The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.]

Temperature (oC) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Percent heat loss from beak 34 35 40 29 36 44 60 48 45 56 43 51 57 60 58 64

a. The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is: (Use decimal notation. Enter the values of the intercept and slope rounded to two decimal places. Use the letter ? to represent the value of the temperature.) ?̂ =

b. Use the equation of the least‑squares regression line to predict beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 25 degrees Celsius. Enter your answer rounded to two decimal places. beak heat as a percent of total body heat loss=

c. What percent of the variation in beak heat loss is explained by the straight-line relationship with temperature? Enter your answer rounded to two decimal places. percent of variation in beak heat loss explained by the equation= %

d. Find the correlation ? between beak heat loss and temperature. Enter your answer rounded to three decimal places. ?=

What statistical test is most appropriate if you want to examine whether there is a difference in graduation rates (percentages) between public and private high schools in your state of residence? Assume the data meets the assumptions for a parametric test.

A criminologist is interested in the effects of unemployment and policing on murder and has run the following multiple regression:

a. What is the Y-intercept? Interpret your results.

b. Which variables are significant at the 0.05 level?

c. What is the predicted homicide rate for a city with an unemployment rate of 5% and 250 police officers per 100,000 population?

Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money that people spend in thrift shops. He takes a small sample of 8 individuals and asks them to report how much money they had in their pockets the last time they went shopping at a thrift store. Here are the data:


27, 22, 11, 19, 20, 19, 25, 21.

Find the upper bound of a 95% confidence interval for the true mean amount of money individuals carry with them to thrift stores, to two decimal places. Take all calculations toward the final answer to three decimal places.

Identify the parameter p in the following binomial distribution scenario. The probability of buying a movie ticket with a popcorn coupon is 0.676, and the probability of buying a movie ticket without a popcorn coupon is 0.324. If you buy 25movie tickets, we want to know the probability that more than 16 of the tickets have popcorn coupons. (Consider tickets with popcorn coupons as successes in the binomial distribution.)

3. Scores on a statistics exam are given: 85 72 92 90 74 65 68 59 74 85 63 79 81 92 95 74 88 55   

Use this data to calculate the:

A) mean __________ B) median ________ C) mode ________ D) range ________

E) standard deviation _________ F) find the z-score for a test grade of 90._______

G) Construct a stem and leaf display using this data.

H) Construct a box and whisker plot using this data.

I) Construct a 90% confidence interval for u.

J) Does this data provide sufficient evidence at the a = .05 level of significance to conclude that the mean score is greater than 75?

K) State the appropriate hypotheses to conduct the test:

ii   Calculate the value of the test-statistic

iii. Give the p-value of the test

iv. Using a 5% significance level, what is your conclusion? Why?

A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of 25°F. However, it is hoped that the new thermostat might be more dependable in the sense that it will hold temperatures closer to 25°F. One frozen food case was equipped with the new thermostat, and a random sample of 26 temperature readings gave a sample variance of 5.1. Another similar frozen food case was equipped with the old thermostat, and a random sample of 16 temperature readings gave a sample variance of 12.8. Test the claim that the population variance of the old thermostat temperature readings is larger than that for the new thermostat. Use a 5% level of significance. How could your test conclusion relate to the question regarding the dependability of the temperature readings? (Let population 1 refer to data from the old thermostat.)

(a) What is the level of significance?

State the null and alternate hypotheses.

H0: σ12 = σ22; H1: σ12 < σ22

H0: σ12 = σ22; H1: σ12 ≠ σ22

H0: σ12 = σ22; H1: σ12 > σ22

H0: σ12 > σ22; H1: σ12 = σ22

(b) Find the value of the sample F statistic. (Round your answer to two decimal places.) What are the degrees of freedom?

dfN =

dfD = What assumptions are you making about the original distribution?

The populations follow independent normal distributions. We have random samples from each population.

The populations follow independent normal distributions. The populations follow independent chi-square distributions. We have random samples from each population.

The populations follow dependent normal distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.)

p-value > 0.100

0.050 < p-value < 0.100

0.025 < p-value < 0.050

0.010 < p-value < 0.025

0.001 < p-value < 0.010

p-value < 0.001

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.

Reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.

Fail to reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.

Fail to reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.

As concrete​ cures, it gains strength. The following data represent the​ 7-day and​ 28-day strength in pounds per square inch​ (psi) of a certain type of concrete. Complete parts​ (a) through​ (f) below. ​7-Day Strength​ (psi), x 2480 3330 2620 3380 3390 ​28-Day Strength​ (psi), y 4120 4850 4190 5020 5220 ​(a) Treating the​ 7-day strength as the explanatory​ variable, x, use technology to determine the estimates of beta 0 and beta 1. beta 0almost equalsb 0equals nothing ​(Round to one decimal place as​ needed.) beta 1almost equalsb 1equals nothing ​(Round to four decimal places as​ needed.) Estimate error? P value? Upper? Lower?

v. Find the margin of error given the following: 99% confidence interval;

n = 68, x bar = 4156 and Std dev. = 839. ________

a. 1298    b.   237    c. 262    d. 8

vi. When do Type II errors occur?________

a. We decide to reject the null hypothesis when the null hypothesis was actually true.

b.   We fail to reject the null hypothesis when the null hypothesis is actually false.

c.   They occur in both cases.

vii. A standard score of z = 1.00 for an observation means: _________

a. The mean of the distribution lies 1 standard deviations below the observation.

b. The observation lies 1 standard deviations below the mean.

c. The observation lies 1 standard deviations above the mean.

d. The observation lies 1 means below the standard deviation.

viii. Given a 90% and a 95% confidence interval, which of the following is true?

1.   The 90% confidence interval is wider than the 95% confidence interval.
2. There is a better chance that the true mean will be found in the 95% confidence interval.

3. None of the above.

ix. The number of hours per week that high school juniors watch TV is normally distributed with a mean of 8 hours and a standard deviation of 2 hours. If 100 students are chosen at random, find the probability that the mean for that sample is between 8.2 and 8.8

1. 0.1598     b. 0.1586     c. 0.1156    d. 0.1152

Note: standard deviation/ the square root of n.

Check out the Central Limit Theorem

Using basic demographic information (age, household income, marital status, etc.), you collect a random sample size 190 customers who accepted a special balance transfer offer from a major credit card company six months ago. The company wants to determine if there is evidence that it would profit by offering the deal to the population of customers with those same demographic characteristics. The sample mean balance transfer amount is 1,935 with a sample standard deviation of 424. Based on the information above, if the company were to perform a hypothesis test at α = 0.05, what is the largest value it could specify in the null hypothesis and still fail to reject the null hypothesis? Hint: Think about the relationship between hypothesis tests and intervals. Specifically, think about how a test done at alpha equals 0.05 would relate to a 95% confidence interval?

1.      Out of 500 people sampled, 140 received flu vaccinations this year. Based on this, construct a 95% confidence interval for the true population proportion of people who received flu vaccinations this year.
Give your answers as decimals, to three places
< p <

2.      You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly more than 0.68. You use a significance level of α=0.05α=0.05.
                                                       H0:p=0.68H0:p=0.68
                                                       H1:p>0.68H1:p>0.68

You obtain a sample of size n=432n=432 in which there are 314 successes.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is... less than (or equal to) ααgreater than αα
This test statistic leads to a decision to... reject the nullaccept the nullfail to reject the null                              As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is more than 0.68.

There is not sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is more than 0.68.

The sample data support the claim that the proportion of men over 50 who regularly have their prostate examined is more than 0.68.

There is not sufficient sample evidence to support the claim that the proportion of men over 50 who regularly have their prostate examined is more than 0.68.

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 47.3 for a sample of size 1066 and standard deviation 6.8. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level).
Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

partial credit, 14.1.19-T The accompanying data represent the total compensation for 12 randomly selected chief executive officers​ (CEOs) and the​ company's stock performance. Use the data to complete parts​ (a) through​ (d). LOADING... Click the icon to view the data table. ​(a) Treating compensation as the explanatory​ variable, x, use technology to determine the estimates of beta 0 and beta 1. The estimate of beta 1 is nothing. ​(Round to three decimal places as​ needed.) Enter your answer in the answer box and then click Check Answer. 7 parts remaining Data Table of Compensation and Stock Performance Company Compensation ​(millions of​ dollars) Stock Return​ (%) A 13.77 72.76 B 4.37 62.14 C 7.43 141.63 D 1.06 36.35 E 1.88 11.96 F 2.01 29.23 G 11.73 0.75 H 7.93 69.86 I 8.32 51.46 J 4.57 56.66 K 21.48 29.97 L 5.76 34.03

Consider the following hypothesis statement using alphaequals0.05 and data from two independent samples. Assume the population variances are not equal and the populations are normally distributed. Complete parts a and b. Upper H 0 : mu 1 minus mu 2 equals 0 x overbar 1 equals 115.1 x overbar 2 equals 122.0 Upper H 1 : mu 1 minus mu 2 not equals 0 s 1 equals 25.6 s 2 equals 14.5 n 1 equals 15 n 2 equals 21 a. Calculate the appropriate test statistic and interpret the result.