Let's assume that the average length of all commercials aired on Hulu is 78 seconds. From a sample of 46 commercials aired during sitcoms, it was found that the average length of those commercials was 76 seconds with a standard deviation of 6.1 seconds. At the 5% significance level, does this data provide sufficient evidence to conclude that the mean length of sitcom commercials is different from 78 seconds?

Step 1: Stating what we are testing Step 2: Stating H₀, H_a, and alpha (α) Step 3: Stating the assumptions of the procedureStep 4: Stating whether we are using a z or t procedure and why

Step 5: Providing calculator output (make sure to include all the numbers mentioned in the template in the notes) Step 6: Interpreting results

Step 7: Stating what type of error we would be making and what it means Step 8: Stating the power of the test

a) Plot the histogram, frequency polygon and cumulative frequency polygon.

b) Compute the sample mean, sample variance and sample standard deviation

c) estimate the median from cumulative frequency distribution and mode from the histogram.

d) is this distribution symmetrical or skewed?

e) What percent of the student course load is expected to fall with in 3 standard deviations from the mean?

8. Why is it important to assess whether missing values are randomly distributed throughout the participants and measures? Or in other words, why is it important to understand what processes lead to missing values?

Can someone send me a screen shot of how to input this into SPSS data and variable view to obtain the information provided below?

Question 1

The nominal scale of measurement is used to measure academic program in this example because data collected for the students is nothing but the names of their major subjects or classes and their status of mood whether they are nervous or excited.

Question 2

The nominal scale of measurement is used to measure feeling about PSY 3002 because the feeling is explained by two categories such as nervous and excited.

Question 3

This scenario required a Chi-square test of independence between two categorical variables. For this scenario, two categories are given as major subject and feeling. Here, we have to check the hypothesis whether the two categorical variables major subject of student and feeling of a student are independent of each other or not.

Question 4

For this scenario, the null and alternative hypotheses are given as below:

Null hypothesis: H₀: The two categorical variables major subject of student and the feeling of the student are independent of each other.

Alternative hypothesis: H_a: The two categorical variables major subject of student and feeling of student are not independent from each other.

We can also write these hypotheses as below:

Null hypothesis: H₀: There is no any relationship between two categorical variables such as major subject of student and feeling of student.

Alternative hypothesis: H_a: There is a relationship between the two categorical variables such as major subject of student and feeling of student.

Question 5

The Chi square test statistic is given as 16.94235589.

Question 6

Number of rows = r = 2

Number of columns = c = 2

Degrees of freedom = (r – 1)*(c – 1) = (2 – 1)*(2 – 1) = 1*1 = 1

Degrees of freedom = 1

Question 7

P-value = 0.0000385

(by using Chi square table or excel)

Question 8

Reject the null hypothesis because p-value is less than alpha value 0.05.

Question 9

Yes, results are statistically significant because p-value for this test is given as 0.0000385 which is less than alpha value 0.05.

Question 10

There is sufficient evidence to conclude that there is a relationship between the two categorical variables such as major subject of student and feeling of student.

There is sufficient evidence to conclude that two categorical variables major subject of student and feeling of student are not independent from each other.

Required output for Chi square test is given as below:

The data below are for 30 people. The independent variable is “age” and the dependent variable is “systolic blood pressure.” Also, note that the variables are presented in the form of vectors that can be used in R.

age=c(39,47,45,47,65,46,67,42,67,56,64,56,59,34,42,48,45,17,20,19,36,50,39,21,44,53,63,29,25,69)

systolic.BP=c(144,20,138,145,162,142,170,124,158,154,162,150,140,110,128,130,135,114,116,124,136,142,120,120,160,158,144,130,125,175)

1. Using R, develop and show a scatterplot of systolic blood pressure (dependent variable) by age (independent variable), and calculate the correlation between these two variables.
2. Assume that these data are “straight enough” to model using a linear regression line. Develop and show that model (write out the model in the terms of the problem), and also show in a plot the line that best fits these data.
3. Plot the residuals and comment on what you see as to how appropriate the model is.
4. Using a boxplot, determine if there are any outliers in systolic blood pressure. If so, point out which points are outliers, if any.
5. Assuming there is at least one outlier in systolic blood pressure, remove that outlier and re-do parts a) through c) again using the remaining data without the outlier(s). State and comment on this second model.
6. In your second model, explain in the context of age and systolic blood pressure what the slope of your fitted line means. Also, for your second model, calculate R² (the coefficient of determination), and explain what that means in the context of your second model.

In a study entitled How Undergraduate Students Use Credit Cards, Sallie Mae reported that undergraduate students have a mean credit card balance of $3173. This figure was an all-time high and had increased 44% over the previous five years. Assume that a current study is being conducted to determine whether it can be concluded that the mean credit card balance for undergraduate students has continued to increase to the April 2009 report.

Based upon previous studies, the population standard deviation was $1000.

A sample was selected of 180 undergraduate students with a sample mean credit card balance of $3325.

Note: use this excel workbook (Sheet "Known SD - Cards") to assist you.

https://drive.google.com/file/d/18bWI0MaoO6VAdhGI6SW0CoE6ws3XwCs3/view

. What is the hypothesis test of the mean ?

B. What is the type of 'tail' test ?

C. What is the p-value? (please round up to three decimal places)

D. With a confidence level of .05, what is your decision regarding H_o ?

E. Based upon the data and a confidence level of .05, is the following statement true or false ?

"The current population mean credit card balance for undergraduate students has increased compared to the previous all-time high of $3173 reported in April 2009."

F. With a confidence level of .01, what is your decision regarding H_o ?

You receive a brochure from a large university. The brochure indicates that the mean class size for​ full-time faculty is fewer than

3333

students. You want to test this claim. You randomly select

1818

classes taught by​ full-time faculty and determine the class size of each. The results are shown in the table below. At

alphaαequals=0.100.10​,

can you support the​ university's claim? Complete parts​ (a) through​ (d) below. Assume the population is normally distributed.

​(a) Write the claim mathematically and identify

Upper H 0H0

and

Upper H Subscript aHa.

Which of the following correctly states

Upper H 0H0

and

Upper H Subscript aHa​?

A.

Upper H 0H0​:

muμequals=3333

Upper H Subscript aHa​:

muμless than<3333

B.

Upper H 0H0​:

muμequals=3333

Upper H Subscript aHa​:

muμnot equals≠3333

C.

Upper H 0H0​:

muμless than<3333

Upper H Subscript aHa​:

muμgreater than or equals≥3333

D.

Upper H 0H0​:

muμgreater than or equals≥3333

Upper H Subscript aHa​:

muμless than<3333

Your answer is correct.

E.

Upper H 0H0​:

muμless than or equals≤3333

Upper H Subscript aHa​:

muμgreater than>3333

F.

Upper H 0H0​:

muμgreater than>3333

Upper H Subscript aHa​:

muμless than or equals≤3333

​(b) Use technology to find the​ P-value.

Pequals=nothing

​(Round to three decimal places as​ needed.)

Using the following data, test the question that an equal number of Democrats, Republicans, and the Independents voted during the most recent election. Test this hypothesis at the .05 level of significance.

Consider two independent random samples with the following results:

n1=158        n2=101

x1=136    x2=45

Use this data to find the 90% confidence interval for the true difference between the population proportions. Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval. Round your answer to three decimal places

Step 2 of 3: Find the margin of error. Round your answer to six decimal places.

Step 3 of 3: Construct the 90% confidence interval. Round your answers to three decimal places.

A state legislator wants to determine whether his voters' performance rating (0 - 100) has changed from last year to this year. The following table shows the legislator's performance from the same ten randomly selected voters for last year and this year. Use this data to find the 80% confidence interval for the true difference between the population means. Assume that the populations of voters' performance ratings are normally distributed for both this year and last year.

Rating (last year)   Rating (this year)
41   59
90   92
58   81
58   55
46   40
84   87
70   61
84   79
51   77
59   64

Step 1 of 4:

Find the point estimate for the population mean of the paired differences. Let x1 be the rating from last year and x2 be the rating from this year and use the formula d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.

Step 2 of 4:Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.

Step 3 of 4:Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 4 of 4:Construct the 80% confidence interval. Round your answers to one decimal place.

Use SAS. Please include the code and the answers.

1. Generate 625 samples of size 961 random numbers from U(1, 9).

For each of these 625 samples calculate the mean:

a) Find the simulated probability that the mean is between 5 and 5.2.

b) Find the mean of the means.

c) Find the standard deviation of the means.

d) Draw the histogram of the means.

Your Toronto Maple Leafs won 30 of 82 games last season (i.e., the 2014-2015 season), giving them a winning percentage of 37%. If we assume this means the probability of the Leafs winning any given game is 0.37, then we can predict how they would have done in a playoff series.

Answer the following questions to determine the probability that the Leafs would have won a best of 7playoff series (i.e., won 4 games) had they made the playoffs last season.

a. Rephrase this question in terms of sequences of 0s and 1s. What is the shortest length of a sequence? What is the longest length of a sequence?

b. Calculate the number of sequences which correspond to the Leafs winning the series. (Note that the answer is not C(7, 4).)

c. Calculate the number of sequences as they relate to this problem. (Note that the answer is not 27 as not all series would last 7 games.)

d. Calculate the probability that the Leafs would win the series.

e. What is your best guess for the probability that the Leafs will ever win the Stanley Cup again (the ultimate prize in the NHL)

2.

A simple random sample with n = 54 provided a sample mean of 22.5 and a

sample standard deviation of 4.4.

a.

Develop a 90% confidence interval for the population mean.

b.

Develop a 95% confidence interval for the population mean.

c.

Develop a 99% confidence interval for the population mean.

d.

What happens to the margin of error and the confidence interval as the

confidence level is increased?

All answers were generated using 1,000 trials and native Excel functionality.) Suppose that the price of a share of a particular stock listed on the New York Stock Exchange is currently $39. The following probability distribution shows how the price per share is expected to change over a three-month period: Stock Price Change ($) Probability –2 0.05 –2 0.10 0 0.25 +1 0.20 +2 0.20 +3 0.10 +4 0.10 (a) Construct a spreadsheet simulation model that computes the value of the stock price in 3 months, 6 months, 9 months, and 12 months under the assumption that the change in stock price over any three-month period is independent of the change in stock price over any other three-month period. For a current price of $39 per share, what is the average stock price per share 12 months from now? What is the standard deviation of the stock price 12 months from now? Based on the model assumptions, what are the lowest and highest possible prices for this stock in 12 months?