A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.8 years, and standard deviation of 0.7 years.

If you randomly purchase one item, what is the probability it will last longer than 6 years? (Give answer to 4 decimal places.)

Students in a statistics class took their first test. The following are the score they earned. Create a histogram for the data and describe the findings Scores(62,87,81,69,69 ,87,60,45,95,76,76 62,71,65,67,67,72,80,40,77,87,58 84,73,90,64,64,89)

a)Find the mean, median, and modal class.

b)What is inter quartile range?

c)What is standard deviation of the test score?

d)Is the score of 40 unusual? Why?

We wish to create a 95% confidence interval for the proportion. A sample of 50 gives a proportion of 0.2. Find the upper value for the confidence interval. Round to 3 decimal places.

1. Consider the experiment of first drawing one card from a single suit and then rolling a single die

a. How many simple events are possible ?

b. List the out sample space .

c. What is the probability of picking the same value card as die roll ?

d. What is the probability of picking a different number card than value rolled ?

e. What is the probability of obtaining a combined value of less than ten (assume that face cards are worth 10 and the ace is worth 11

Many people believe that the average number of Facebook friends is 135. The population standard deviation is 37.7. A random sample of 38 high school students in a particular county revealed that the average number of Facebook friends was 151. At α=0.05, is there sufficient evidence to conclude that the mean number of friends is greater than 135?

(a)State the hypotheses and identify the claim.

(b)Find the critical value.

(c)Compute the test value.

(d)Make the decision.

(e)Summarize the results.

The following data are from an experiment designed to investigate the perception of corporate ethical values among individuals who are in marketing. Three groups are considered: management, research and advertising (higher scores indicate higher ethical values).

1. Compute the values identified below (to 1 decimal, if necessary).
   

   Sum of Squares, Treatment
   Sum of Squares, Error
   Mean Squares, Treatment
   Mean Squares, Error

   
   
2. Use  = .05 to test for a significant difference in perception among the three groups.
   
   Calculate the value of the test statistic (to 2 decimals).
   
   
   c. The p-value is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6
   
   What is your conclusion?
   Select : Conclude the mean perception scores for the three groups are not all the same or Cannot conclude there are differences among the mean perception scores for the three groups
3. Using  = .05, determine where differences between the mean perception scores occur.
   
   Calculate Fisher's LSD value (to 2 decimals).
   
   
   Test whether there is a significant difference between the means for marketing managers (1), marketing research specialists (2), and advertising specialists (3).
   

   Difference	Absolute Value	Conclusion
   x 1 - x2		Select Significant difference No significant differenceItem 10
   x1 - x3		Select Significant difference No significant differenceItem 12
   x 2 - x3

In a survey of 1373 ​people, 930 people said they voted in a recent presidential election. Voting records show that 65​% of eligible voters actually did vote. Given that 65​% of eligible voters actually did​ vote, (a) find the probability that among 1373 randomly selected​ voters, at least 930 actually did vote.​ (b) What do the results from part​ (a) suggest? ​(a) ​P(Xgreater than or equals930​)equals nothing ​(Round to four decimal places as​ needed.) ​(b) What does the result from part​ (a) suggest?

A. Some people are being less than honest because ​P(xgreater than or equals930​) is at least​ 1%.

B. People are being honest because the probability of ​P(xgreater than or equals930​) is at least​ 1%.

C. Some people are being less than honest because ​P(xgreater than or equals930​) is less than​ 5%.

D. People are being honest because the probability of ​P(xgreater than or equals930​) is less than​ 5%.

Consider the paired sample {(3, 1),(3, 5),(6, 6),(6, 8),(7, 10)}. Do the following by hand (you may use a basic calculator, but not a statistical program).

(a) Find estimates βˆ 0 and βˆ 1 of the regression parameters β0 and β1.

(b) Make a rough sketch of the data and regression line.

(c) Predict the value of y when x = 5.

(d) Predict the value of y when x = 15.

(e) Which prediction (part c or d) do you trust more? Why?

(f) For the data point (3, 5), calculate the residual i .

(g) Perform a test of H0 : β1 = 0 vs HA : β1 6= 0. Use α = 0.05.

Question 5

An urban planner is researching commute times in the San Francisco Bay Area to find out if commute times have increased. In which of the following situations could the urban planner use a hypothesis test for a population mean? Check all that apply.

1. The urban planner asks a simple random sample of 110 commuters in the San Francisco Bay Area if they believe their commute time has increased in the past year. The urban planner will compute the proportion of commuters who believe their commute time has increased in the past year.
2. The urban planner collects travel times from a random sample of 125 commuters in the San Francisco Bay Area. A traffic study from last year claimed that the average commute time in the San Francisco Bay Area is 45 minutes. The urban planner will see if there is evidence the average commute time is greater than 45 minutes.
3. The urban planner asks a random sample of 100 commuters in the San Francisco Bay Area to record travel times on a Tuesday morning. One year later, the urban planner asks the same 100 commuters to record travel times on a Tuesday morning. The urban planner will see if the difference in commute times shows an increase.

Question 6

The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food and drugs for consumer safety. One thing the FDA regulates is the allowable insect parts in various foods. You may be surprised to know that much of the processed food we eat contains insect parts. An example is flour. When wheat is ground into flour, insects that were in the wheat are ground up as well.

The mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. If the FDA finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption.

The null hypothesis is that the mean number of insect parts per 100 grams is 75. The alternative hypothesis is that the mean number of insect parts per 100 grams is greater than 75.

Is the following a Type I error or a Type II error or neither?

The test fails to show that the mean number of insect parts is greater than 75 per 100 grams when it is.

1. Type I error
2. Type II error
3. Neither

Question 7

Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the age of first time expectant mothers. Suppose that CHDS finds the average age for a first time mother is 26 years old. Suppose also that, in 2015, a random sample of 50 expectant mothers have mean age of 26.5 years old, with a standard deviation of 1.9 years. At the 5% significance level, we conduct a one-sided T-test to see if the mean age in 2015 is significantly greater than 26 years old. Statistical software tells us that the p-value = 0.034.

Which of the following is the most appropriate conclusion?

1. There is a 3.4% chance that a random sample of 50 expectant mothers will have a mean age of 26.5 years old or greater if the mean age for a first time mother is 26 years old.
2. There is a 3.4% chance that mean age for all expectant mothers is 26 years old in 2015.
3. There is a 3.4% chance that mean age for all expectant mothers is 26.5 years old in 2015.
4. There is 3.4% chance that the population of expectant mothers will have a mean age of 26.5 years old or greater in 2015 if the mean age for all expectant mothers was 26 years old in 1959.

Question 8

Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 40 expectant mothers have mean weight increase of 16 pounds in the second trimester, with a standard deviation of 6 pounds. At the 5% significance level, we can conduct a one-sided T-test to see if the mean weight increase in 2015 is greater than 14 pounds. Statistical software tells us that the p-value = 0.021.

Which of the following is the most appropriate conclusion?

1. There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds.
2. There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 14 pounds in 2015.
3. There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 16 pounds in 2015.
4. There is 2.1% chance that the population of expectant mothers will have a mean weight increase of 16 pounds or greater in 2015 if the mean second trimester weight gain for all expectant mothers was 14 pounds in 1959.

Question 9

A researcher conducts an experiment on human memory and recruits 15 people to participate in her study. She performs the experiment and analyzes the results. She uses a t-test for a mean and obtains a p-value of 0.17.

Which of the following is a reasonable interpretation of her results?

1. This suggests that her experimental treatment has no effect on memory.
2. If there is a treatment effect, the sample size was too small to detect it.
3. She should reject the null hypothesis.
4. There is evidence of a small effect on memory by her experimental treatment.

Question 10

A criminal investigator conducts a study on the accuracy of fingerprint matching and recruits a random sample of 35 people to participate. Since this is a random sample of people, we don’t expect the fingerprints to match the comparison print. In the general population, a score of 80 indicates no match. Scores greater than 80 indicate a match. If the mean score suggests a match, then the fingerprint matching criteria are not accurate.

The null hypothesis is that the mean match score is 80. The alternative hypothesis is that the mean match score is greater than 80.

The criminal investigator chooses a 5% level of significance. She performs the experiment and analyzes the results. She uses a t-test for a mean and obtains a p-value of 0.04.

Which of the following is a reasonable interpretation of her results?

1. This suggests that there is evidence that the mean match score is greater than 80. This suggests that the fingerprint matching criteria are not accurate.
2. If there is a treatment effect, the sample size was too small to detect it. This suggests that we need a larger sample to determine if the fingerprint matching criteria are not accurate.
3. She cannot reject the null hypothesis. This suggests that the fingerprint matching criteria could be accurate.
4. This suggests that there is evidence that the mean match score is equal to 80. This suggests that the fingerprint matching criteria is accurate.

Question 11

A group of 42 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic drinks they have in a typical week. The purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. In particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of U.S. college students in general, which is estimated to be 4.73.

The group of 42 students in the study reported an average of 5.31 drinks per with a standard deviation of 3.93 drinks.

Find the p-value for the hypothesis test.

The p-value should be rounded to 4-decimal places.

Question 12

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 240 people from the 2000 U.S. Census who reported a non-zero commute time.

In this sample the mean commute time is 28.9 minutes with a standard deviation of 19.0 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance.

What is the p-value for this hypothesis test?

Your answer should be rounded to 4 decimal places.

A random sample of ?n measurements was selected from a population with standard deviation ?=11.7 and unknown mean ?. Calculate a 95% confidence interval for ? for each of the following situations:

(a) ?=60, ?=85
≤?≤

(b)  ?=75, ?=85
≤?≤

(c)  ?=100, ?=85
≤?≤

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 67 professional actors, it was found that 44 were extroverts.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 5% confident that the true proportion of actors who are extroverts falls above this interval.We are 5% confident that the true proportion of actors who are extroverts falls within this interval.    We are 95% confident that the true proportion of actors who are extroverts falls within this interval.We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

(c) Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.    Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.

Ten males and ten females were interviewed for a mid-level management position and their interview times were recorded in minutes . Shown below are descriptive statistics for the males and females. Your task is to determine of there was a significant difference in the average length of the interviews given to men and women.

Males.     Females

a. Give your obtained values of the test statistics=

b. give the critical values of the test statistics for the .05 level of significance=

c. Do the groups differ significantly? (Type YES or NO)

a. Using the original values, compute the Euclidean distance between the first two observations. (Round intermediate calculations to at least 4 decimal places and your final answer to 2 decimal places.)

Euclidean distance between observations 1 and 2 ___________

b. Using the original values, compute the Manhattan distance between the first two observations. (Round your final answer to 2 decimal places.)

Manhattan distance between observations 1 and 2 ___________

c. Use z-scores to standardize the values, and then compute the Euclidean distance between the first two observations. (Round intermediate calculations to at least 4 decimal places and your final answer to 2 decimal places.)

The z-score standardized euclidean distance between observations 1 and 2 ___________

d. Use the min-max transformation to normalize the values, and then compute the Euclidean distance between the first two observations. (Round intermediate calculations to at least 4 decimal places and your final answer to 2 decimal places.)

The min-max standardized euclidean distance between observations 1 and 2 ___________

The accompanying data file contains 10 observations with two variables, x₁ and x₂.

The mean age of Senators in the 109th Congress was 60.35 years. A random sample of 40 senators from various state senates had an average age of 55.4 years, and the population standard deviation is 6.5 years. At α= 0.05, is there sufficient evidence that state senators are on average younger than the Senators in Washington?

We should use

Left- tailed test

Right- Tailed Test

Two- tailed Test