The scores of students on the ACT (American College Testing)college entrance examination in a recent year had the normal distribution with meanμ= 18 and standard deviationσ= 6. 100 students are randomly selected from all who took the test

a.What is the probability that the mean score for the 100 students is between 17and 19 (including 17 and 19)?

b.A student is eligible for an honor program if his/her score is higher than 25.Find an approximation to the probability that at least 15 students of the 100 students are eligible for the honor program.

c.If the sample size is 4 (rather than 100), what is the probability that more than50% (not include 50%) students are eligible for the honor program?

A magazine provided results from a poll of 1500 adults who were asked to identify their favorite pie. Among the 1500 ​respondents, 11% chose chocolate​ pie, and the margin of error was given as plus or minus 4percentage points. What values do ModifyingAbove p with caret​,ModifyingAbove q with caret n, E, and p​ represent? If the confidence level is 99%, what is the value of alpha?

Microplastics have been found in both tap water and bottled water.
Bottled water results A study analyzed 259 bottles and found an average of 320 plastic particles for every liter of water being sold. The associated standard deviation was 327. (Yes, the standard deviation is larger than the mean.)
Tap water results In a similar study, 30 tap water samples were analyzed. The average number of plastic particles found in each liter in the United States was 8.8 with a standard deviation of 2.3.
Conduct a hypothesis to evaluate if there is a difference between the average number of plastic particles in water bottles vs tap water.

What type of test should be run?

• Paired T-test
• 2 Sample T-test
• T-test
• 1 Proportion Z-test
• 2 Proportion Z-test

What are the hypotheses for this test?

• Ho: μ_bottled = μ_tap
  Ha: μ_bottled > μ_tap
• Ho: μ_bottled = μ_tap
  Ha: μ_bottled < μ_tap
• Ho: μ_bottled = μ_tap
  Ha: μ_bottled ≠ μ_tap

The test statistic for the hypothesis test is:  (please round to two decimal places)
The p-value for the hypothesis test is:  (please round to four decimal places)
Interpret the result of the hypothesis test in the context of the study:

• We reject the claim that the average number of plastic particles found in tap water and bottled water is the same.
• We fail to reject the claim that the average number of plastic particles found in tap water and bottled water is the same.

a give the probability of getting a sequence of Gold then Silver then Blue on three consecutive spins. b.If the wheel is spun four times, give the probability of getting Blue only on the fourth spin. c.Give the probability of getting at least one Blue on five consecutive spins. there are 4 red spaces, 2 blue, one gold, and one silver space.

A boot making company produces women’s cowboy boots. The boots come in either square toe or round toe options. In an effort to estimate the proportion of boots sales at their Calgary locations that are square toe, a random sample of 140 boot sales was collected. It was discovered that 65 sales were for square toe boots. Construct a 98% confidence interval to estimate the proportion of Calgarians who purchase square toe boots. Keep 3 decimal places for all calculated values.

The results from a two-factor experiment can be presented in a matrix with the levels of one factor forming the rows and the levels of the second factor forming the columns, with a separate sample in each of the matrix cells. Demonstrate this with your own example, and describe what is meant by the main effects for each factor and the interaction between factors based on the numbers that you choose to plug in for each one of the cells.

Suppose that in a city of 120,000 people the average income is 40,000 (dollars). Use the basic estimates we learned for ”tail probabilities” to:

(a) Find an upper bound for the number of people in the city with income above 60,000 dollars.

(b) Find a smaller upper bound, given that the standard deviation of the incomes is 1000 dollars.

(c) Show that the distribution of incomes in the city cannot be a normal distribution!

A statistical program is recommended.

The owner of a movie theater company would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

(a)

Use α = 0.01 to test the hypotheses

for the model

y = β₀ + β₁x₁ + β₂x₂ + ε,

where

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.Do not reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.     Reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables. Do not reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.

(b)

Use α = 0.05 to test the significance of

β₁.

State the null and alternative hypotheses.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that β₁ is significant.Do not reject H₀. There is insufficient evidence to conclude that β₁ is significant.     Reject H₀. There is sufficient evidence to conclude that β₁ is significant.Do not reject H₀. There is sufficient evidence to conclude that β₁ is significant.

Should

x₁

be dropped from the model?

YesNo   

(c)

Use α = 0.05 to test the significance of

β₂.

State the null and alternative hypotheses.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that β₂ is significant.Reject H₀. There is insufficient evidence to conclude that β₂ is significant.     Do not reject H₀. There is sufficient evidence to conclude that β₂ is significant.Do not reject H₀. There is insufficient evidence to conclude that β₂ is significant.

Should

x₂

be dropped from the model?

YesNo   

A study is run to estimate the average number of toilet paper rolls a typical U.S. household currently have. Say a sample of 10 households is selected last month and they reported the number of toilet paper (in rolls) as follows.

                       75         56        50        94        65       111      97        88            103        98

1. Assume the average amount of toilet paper a household usually have is 55 rolls at national level. Test whether the mean number of toilet paper rolls in this sample is significantly different from the national level? Use alpha level of .05.
2. Based on your results from part (a), without calculating the confidence interval, describe how the confidence interval of the average number of toilet paper at national level.  (Hint: interpret the meaning of confidence interval in relation to a hypothesis test.)

A survey of high school students revealed that the numbers of soft drinks consumed per month was normally distributed with mean 25 and standard deviation 15. A sample of 36 students was selected. What is the probability that the average number of soft drinks consumed per month for the sample was between 28.1 and 30 soft drinks?

Write only a number as your answer. Round to 4 decimal places (for example 0.0048). Do not write as a percentage.

a. Generate a model for college GPA as a function of the other three variables.

b. Is this model useful? Justify your conclusion.

c. Are any of the variables not useful predictors? Why?

In 2011 home prices and mortgage rates dropped so low that in a number of cities the monthly cost of owning a home was less expensive than renting. The following data show the average asking rent for 10 markets and the monthly mortgage on the median priced home (including taxes and insurance) for 10 cities where the average monthly mortgage payment was less than the average asking rent (The Wall Street Journal, November 26–27, 2011).

1   26.5
1   28.7
1   25.1
1   29.1
1   27.2
2   31.2
2   28.3
2   30.8
2   27.9
2   29.6
3   27.9
3   25.1
3   28.5
3   24.2
3   26.5
4   30.8
4   29.6
4   32.4
4   31.7
4   32.8

Q1:

• Test for equal variations using the Bartlett test.
Calculating the value of the test statistic
o Finding critical (tabular) values
o Determine the area rejecting the null hypothesis
the decision
Conclusion

A sociologist was hired by a large city hospital to investigate the relationship between the number of
unauthorized days that employees are absent per year and the distance (miles) between home and
work for the employees. A sample of 6 employees was chosen, and the following data were collected.
Distance to work (miles) 1 3 4 6 8 10
Number of days absent 8 5 8 7 6 3

e. Compute the correlation coefficient.
f. Conduct a t-test at a 0.05 level of significance to test for a significant relationship between
distance to work and number of days absent. State your conclusion.
g. Conduct an F-test at a 0.05 level of significance to test for a significant relationship between
distance to work and number of days absent. State your conclusion.
h. Did you get the same conclusion for the t-test and the F-test? Will this always be the case for a
test for significance of the relationship in a simple linear regression?

I have the following statistics problem.  

Katrina wants to estimate the proportion of adult Americans who read at least 10 books last year. To do so, she obtains a simple random sample of 100 adult Americans and constructs a 95% confidence interval. Mathew also wants to estimate the proportion of adult Americans who read at least 10 books last year. He obtains a simple random sample of 400 adult Americans and constructs a 99% confidence level. Assuming both Katrina and Mathew obtained the same point estimate, whose estimate will have the smaller margin of error (Make sure to answer the following parts). 1) make up a point estimate for Katrina and Mathew's study. report the point estimate used 2) in order to have the same point estimate, what will be the number of successes in Katrina's study? what will be the number of successes in Mathew's study? 3) compute the confidence interval for both person as the problem described. who has the smaller margin of error? how can you tell?

I have the n, the ‘fish symbol’ and the confidence interval and the confidence interval critical value and the ‘fish’ symbol divided by 2

I’m struggling with the point estimate and the number of success for both and who has the smallest margin of error. I am