ONE SAMPLE T-TEST

Assignment 1: Change in Mood Following a Romantic Movie Clip

A researcher asks participants to watch a short romantic movie clip. The movie clip depicts a romantic scene ending with two long-lost lovers embracing in a kiss. After the short romantic movie clip, participants are asked to indicate how the romantic movie clip has affected their mood on a bipolar scale ranging from -3 (much worse mood) to +3 (much better mood), with 0 indicating no change in mood. The results are given below. It was assumed that the average participant would give a rating of 0 if there were no change in mood. Test whether or not participants reported a significant change in mood at a .05 level of significance using a two­tailed test.

SCORES: -3, -3, -3, -3, -3, -3, -3, -3, -3,

-2, -2, -2, -2, -2, -2, -2, -2, -2,

2,

-1, -1, -1, -1, -1, -1, -1

0, 0, 0, 0, 0, 0, 0, 0, 0, 0

With regard to the SPSS exercise, answer the following questions:

Based on the SPSS output, state the following values:

Sample size, Sample mean, Sample standard deviation, Estimated standard error                                                 

Based on the table shown in SPSS, state the following values associated with the test statistic:

Mean difference, t obtained (t), Degrees of freedom (df), Significance (2-tailed)

2,006 persons are cross classified by disease and exposure.

Our outcome of interest is having the disease.

Use the following 2 x 2 table to answer questions below.

a. What percent of people have disease?

b. What percent of the exposed persons have disease?

c. What is the odds of disease among the exposed?

d. What is the odds of disease among the unexposed?

e. What is the odds ratio of disease among the exposed and unexposed. Interpret the odds ratio and comment whether the exposure is deleterious or protective.

Traditional definition of independence says that events A and B are
independent if and only if P(A n B)=P(A)×P(B). Show that P(A n B)=P(A)×P(B) if
and only if
a. P(A n B’) = P(A) × P(B’)b. P(A’ n B’) = P(A’) × P(B’)
You may use these without proof in your solutions:
o P(A n B’) = P(A) – P(A n B). [This can be proven by first showing that
(A ∩ B ′ ) ∪̇ (A ∩ B) = A and using the Addition Rule.]
o P(A n B) = 1 – P(A’ n B’). [This can be proven by noting that under de
Morgan’s Law, (A n B)’ = A’ n B’.]

A friend of mine is giving a dinner party. His current wine supply includes 12 bottles of zinfandel, 8 of merlot, and 10 of cabernet (he only drinks red wine), all from different wineries.

(a) If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this?
ways

(b) If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this?
ways

(c) If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety?
ways

(d) If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (Round your answer to three decimal places.)


(e) If 6 bottles are randomly selected, what is the probability that all of them are the same variety? (Round your answer to three decimal places.)

Assume the binomial distribution is appropriate. If N = 10 and P = 0.30, the probability of getting at least 8 P events is _________.

Two players (player A and player B) are playing a game against each other repeatedly until one is bankrupt. When a player wins a game they take $1 from the other player. All plays of the game are independent and identical. Suppose player A starts with $6 and player B starts with $6. If player A wins a game with probability 0.5, what is the probability the game ends (someone loses all their money) on exactly the 10th play of the game?

Determine the area under the standard normal curve that lies between:

a. z= -.31 and z=1.61

b. z=-2.01 and z=.26

c. z=-1.20 and z=2.11

d. z=1.92 and z=2.43

Find the value of z_a

a. z_.56=

b. Z_.23=

c. Z_.81=

d. Z_.06=

5.) For the data set

(a) Find the 80th percentile.

(a) Find the 42nd percentile.

(a) Find the 17th percentile.

(a) Find the 65th percentile.

6.) Internet providers: In a survey of 672 homeowners with high-speed Internet, the average monthly cost of a high-speed Internet plan was $52.8 with standard deviation $12.42 Assume the plan costs to be approximately bell-shaped. Estimate the number of plans that cost between $40.38 and $65.22

The table below lists a random sample of 50 speeding tickets on I-25 in Colorado.

Round to the fourth.
a) If a random ticket was selected, what would be the probability that the driver was female?
b) Given that a particular ticket had a male offender, what is the probability that they were more than 20 mph over the limit?
c) Given that a particular ticket was 10-20 mph over the limit, what is the probability that the driver was female?
d) If a random ticket was selected, what would be the probability that the driver was a male?
e) If a random ticket was selected, what would be the probability that the driver is a female and driving 10-20 mph over the limit?
f) If a random ticket was selected, what would be the probability that the driver is a female or driving 0-10 mph over the limit?

Chapter 3 – Numerically Summarizing Data

1. Section 3.1 Measures of Central Tendency

pH in Water:

The acidity of alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The following data represent the pH in samples of bottled water and tap water.

1. Determine the mean, median and mode pH for each type of water.
2. Comment on the differences between the two water types.
3. Suppose the pH of 7.10 in tap water was incorrectly recorded as 1.70. How does this affect the mean? The median?
4. What property of the median does this illustrate?

2. Section 3.2 Measures of Dispersion

pH in Water:

Use the same pH data table in the above question to answer the following.

1. Which type of water has more dispersion in pH using the range as the measure of dispersion?
2. Which type of water has more dispersion in pH using the standard deviation as the measure of dispersion?

3. Section 3.2 Measures of Dispersion

The Empirical Rule:

SAT Math scores have a bell-shaped distribution with a mean of 515 and a standard deviation of 114.

1. What percentage of SAT scores is between 401 and 629?
2. What percentage of SAT scores is less than 401 or greater than 629?

4. Section 3.4 Measures of Position and Outliers

You Explain it – Percentiles & Quartiles:

1. The 5^thpercentile of the weight of males 36 months of age is 12.0 kg.
2. The 95^thpercentile of the length of newborn females is 53.8 cm.

One variable that is measured by online homework systems is the amount of time a student spends on homework for each section of the text. The following is a summary of the number of minutes a student spends for each section of the text for the fall 2014 semester in a college statistics class at UHWO.

Q1 = 42         Q2 = 51.5         Q3 = 72.5

3. Provide an interpretation of these results.
4. Determine and interpret the interquartile range.
5. Suppose a student spends 2 hours doing homework for a section. Is this an outlier?
6. Do you believe that the distribution of time spend doing homework is skewed or symmetric? Explain your answer.

5. Section 3.5 The Five Number Summary & Boxplots

Got a Headache?

The following data represent the weight in grams of a random sample of 25 Tylenol tablets.

1. Construct a boxplot.
2. Use the boxplot and quartiles to describe the shape of the distribution.

(A review on SAS data management) The following is a data set of 12 individuals. And we want to relate the heart rate at rest (Y) to kilograms body weight (X). X Y 90 62 87 41 87 63 73 46 73 53 86 55 100 70 75 47 76 49 87 69 79 41 78 48 Write a program in SAS which read the given data set into SAS library. In your program, create a new data set which is a copy of the first, with the addition of a new variable which represents the weight in pounds (1 kilogram≈2.2 pounds). Use “proc print” to view the data for all three variables. (c) Create a new variable called weight_group which divides the data set into four groups based on the estimated quartiles for the variable weight. The estimated quartiles may be requested using the keywords q1, median, and q3, in the “proc means” statement. (d) Use “proc freq” to summarize the frequency of subjects in each of the four groups. (e) Obtain the mean and standard deviation for the heart rate at rest for each of the four groups. Comment on the results. (f) Produce a scatterplot of the heart rate at rest versus body weight in kilograms. Describe what you see. (g)Fit a straight line model for heart rate at rest versus body weight in kilograms. Comment on the fit of the line.

What does the sigma level capability mean for a process? Explain at least two reasons for the importance of achieving six-sigma capability. explain in detail

From your analysis of Desertia, you conclude that citizens there average $1,000 per month in household disposable income. The Minister of Development for Mountania says that disposable income is the same in his country. To see if the data supports this, your company has sampled 100 households from Mountania and obtained data on household disposable income. Use the Data provided to:

a. ​Derive a frequency distribution of income. Divide by 8
b.​Create a histogram of income
c.​Obtain and fully interpret/explain the sample mean and standard deviation
d.​Test the hypothesis, at the 5% significance level, that Mountania also has a mean of $1,000

You may need to use the appropriate technology to answer this question.

Test the following hypotheses by using the

χ²

goodness of fit test.

A sample of size 200 yielded 80 in category A, 20 in category B, and 100 in category C. Use α = 0.01 and test to see whether the proportions are as stated in

H₀.

(a)

Use the p-value approach.

Find the value of the test statistic.

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

p-value =

State your conclusion.

Reject H₀. We conclude that the proportions are equal to 0.40, 0.40, and 0.20.Reject H₀. We conclude that the proportions differ from 0.40, 0.40, and 0.20.     Do not reject H₀. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20.Do not reject H₀. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20.

(b)

Repeat the test using the critical value approach.

Find the value of the test statistic.

State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail. Round your answers to three decimal places.)

test statistic ≤test statistic ≥

State your conclusion.

Do not reject H₀. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20.Do not reject H₀. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20.     Reject H₀. We conclude that the proportions are equal to 0.40, 0.40, and 0.20.Reject H₀. We conclude that the proportions differ from 0.40, 0.40, and 0.20.