12. An agricultural research company has developed two new types of soy bean seeds, call them "seed A" and "seed B". A study is conducted to determine which will produce a higher mean yield. To test the two types of seed, 20 similar plots of land were randomly placed into one of two groups. One group of ten plots was planted with "seed A", while the other ten plots were planted with "seed B". The yield of each field, in bushels per acre, was recorded in the table below.

1. Conduct a hypothesis test at a 0.050.05 level of significance to determine if the two types of soy beans produce different mean yields.

The test statistic is ________________________
The p-value is____________________________

Construct a 9595% confidence interval for the mean of the differences. Hint: with the data in your lists, use the two-independent sample t-INTERVAL option on your calculator.
__________________to________________________

13. A company owns 9 trucks of various makes and models. The manager recently heard that inflating tires with nitrogen may provide slightly better gas mileage. The manager wants to determine if there is a noticeable increase in the mean gas mileage for the 9 trucks when nitrogen is utilized. Over a period of time, a test is run in which the gas mileage of each truck is recorded both with and without nitrogen in the tires. The gas mileages of the 15 trucks with and without nitrogen in the tires are recorded here. (data is in miles per gallon)

(b) The test statistic is_____________________

(c) The p-value is________________________

14. A professor of nursing wonders if the female nursing students are more likely to drop out of a nursing program than the male nursing students. To check her intuition, several nursing programs are compiled and random samples of both male and female nursing students are selected. Of the 200 male nursing students selected, 17 of them did not attain their nursing degree. Of the 700 female nursing students selected, 68 of them did not attain their nursing degree. Test the claim that the proportion of females not completing their degree is higher than the proportion of males using a level of significance of 0.05.
The test statistic is _________________
The p-value is ____________________

A point estimator is a sample statistic that provides a point estimate of a population parameter. Complete the following statements about point estimators.

Given two unbiased estimators of the same population parameter, the estimator with thelarger expected value   is consistent   .

A point estimator is said to bebiased   if itsexpected value   is equal to the value of the population parameter that it estimates.

A point estimator is said to beunbiased   if, as the sample size is     , the estimator tends to provide better estimates of the population parameter.

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- Using R Randomization Test -

"When waiting to get someone's parking space, have you ever thought that the driver you are waiting for is taking longer than necessary? Ruback and Juieng (1997) ran a simple experiment to examine that question. They hung out in parking lots and recorded the time that it took for a car to leave a parking place. They broke the data down on the basis of whether or not someone in another car was waiting for the space.

The data are positively skewed, because a driver can safely leave a space only so quickly, but, as we all know, they can sometimes take a very long time. But because the data are skewed, we might feel distinctly uncomfortable using a parametric t test. So we will adopt a randomization test."

```{r}
# no waiting records the time it took a driver to leave the parking spot if no one was waiting for the driver
no_waiting <- c(36.30, 42.07, 39.97, 39.33, 33.76, 33.91, 39.65, 84.92, 40.70, 39.65,
39.48, 35.38, 75.07, 36.46, 38.73, 33.88, 34.39, 60.52, 53.63, 50.62)

# waiting records the time it takes a driver to leave if someone was waiting on the driver
waiting <- c(49.48, 43.30, 85.97, 46.92, 49.18, 79.30, 47.35, 46.52, 59.68, 42.89,
49.29, 68.69, 41.61, 46.81, 43.75, 46.55, 42.33, 71.48, 78.95, 42.06)

mean(waiting)
mean(no_waiting)
obs_dif <- mean(waiting) - mean(no_waiting)
```

Conduct a randomization test to test the hypothesis that there is no difference in average time for drivers who have a person waiting vs those who do not have a person waiting, against the alternative that drivers who have a person waiting will take *longer* than if they did not.

Be sure to calculate an empirical p-value and make the appropriate conclusion.

In the manufacturing process of carbon composition resistors historical records indicate that 80% of these components have superior quality, 10% have very good quality, 5% have marginal quality and 5% are poor (non-shippable). A quality control firm implemented changes to the manufacturing plant (like installing dehumidifiers) and several months later a random sample of 1200 carbon composition resistors we gathered and rated. Here’s what was found:

Superior:996 Very good:126 Marginal:48 Poor:30 Total:1200

Answer the following questions below.
(a) Test if there is evidence to suggest that the implemented change changed the distribution. Use α = .05.

(b) Looking at each of the (Xi−Ei)2 , which is the largest and construct a 95% confidence interval the multi- Ei

nomial proportion corresponding this ratio.
(c) Would you believe that the installation of dehumidifiers improved the quality? Briefly explain.

The numbers below represent heights (in feet) of 3-year old elm trees.

5.1, 5.5, 5.8, 6.1, 6.2, 6.4, 6.7, 6.8, 6.9, 7.0,

7.2, 7.3, 7.3, 7.4, 7.5, 7.7, 7.9, 8.1, 8.1, 8.2,

8.3, 8.5, 8.6, 8.6, 8.7, 8.7, 8.9, 8.9, 9.0, 9.1,

9.3, 9.4, 9.6, 9.8, 10.0, 10.2, 10.2

Using the chi-square goodness-of-fit test, determine whether the heights of 3-year old elm trees are normally distributed, at the a = .05 significance level. Also, find the p- value.

Sheldon Pikyeeter has peculiar eating habits. For dinner, he always eats spaghetti 3 times per week, cheese pizza twice a week, Thai chicken one time per week, and tacos once a week. Note: for all questions below, consider each week as starting on Sunday and ending Saturday!

a) For a particular week, Sheldon is going to list all the possible different dinner plans. (Sunday through Saturday). How many weekly dinner plans are on Sheldon’s list?

b) What is the probability that a weekly dinner plan has spaghetti on Monday and pizza on Friday?

c) What is the probability that a weekly dinner plan has taco night before all of the spaghetti nights?

d) What is the probability that all of the spaghetti nights are on consecutive nights in a week?

e) What is the probability that none of the spaghetti dinners are on consecutive nights?

A regression Study involving 32 convenience stores was undertaken to examine the relationship between monthly newspaper advertising expenditures (X) and the number of the customers shopping at the store (Y). A partial ANOVA table is below.

Complete the mission parts of the table.

Test whether or not X and Y are linearly related using the correlation coefficient. Use alpha = .01

What proportion of the variation in the number of customers is left UNEXPLAINED by this model?

At the 1% level of significance, what is the critical value to test the explanatory power of the model?

Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and a standard deviation of 30.9 and 2.7 mpg, respectively. [You may find it useful to reference the z table.]

a. What is the probability that a randomly selected passenger car gets more than 32 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

b. What is the probability that the average mpg of four randomly selected passenger cars is more than 32 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. If four passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 32 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

The situation is as follows: Rent and other associated housing costs, such as utilities, are an important part of the estimated costs of attendance at college. A group of researchers at the Off-Campus Housing department want to estimate the mean monthly rent that unmarried students paid during Winter 2019. During March 2019, they randomly sampled 366 students and found that on average, students paid $348 for rent with a standard deviation of $76. The plot of the sample data showed no extreme skewness or outliers. Calculate a 98% confidence interval estimate for the mean monthly rent of all unmarried students in Winter 2019. QUESTION: What is a 98% confidence interval estimate for the mean monthly rent of all unmarried BYU students in Winter 2019?

1A. State the name of the appropriate estimation procedure.

1B Describe the parameter of interest in the context of the problem.

1C. Name the conditions for the procedure.

1D. Explain how the above conditions are met. (

1E. Write down the confidence level and the t* critical value.

1F. Calculate the margin of error for the interval to two decimal places. Show your work.

1G. Calculate the confidence interval to two decimal places and state it in interval form.

1H. CONCLUDE Interpret your confidence interval in context. Do this by including these three parts in your conclusion:  Level of confidence, Parameter of interest in context, the interval estimate

A study is conducted of the relationship between a newborn’s weight and the amount of cigarette smoking by the mother. A strong, negative relationship is found; that is, the more the mother smokes, the smaller the baby tends to be. Give at least 2 plausible explanations of this result.

A professor has kept track of test scores for students who have attended every class and for students who have missed one or more classes. below are scores collected so far.

perfect: 80,86,85,84,81,92,77,87,82,90,79,82,72,88,82

missed 1+:61,80,65,64,74,78,62,73,58,72,67,71,70,71,66

1. Evaluate the assumptions of normality and homoscedasticity

2. conduct a statistical test to assess if exam scores are different between perfect attenders and those who have missed class

3. What is the meaning of the 95% confidence interval given from the R code. What does the 95% CI explain compared to the hypothesis test and how does the 95% CI relate to the test statistic and p value

1. One‐Sample Univariate Hypothesis Testing of a Mean

Consider a random sample of 5 adults over the age of 25 from a large population, which is normally distributed, where E represents the total years of education completed: ? = [10, 12, 12, 16, 16] Suppose that someone claims that the average person in the population is a college graduate (? = 16).

A. What is the null hypothesis?  What is the alternative hypothesis?

B. Can you reject the null hypothesis at the 10‐percent level of significance?   Can you reject the null hypothesis at the 5‐percent level of significance?   Use the critical value approach.  You can use R for critical values, but you must show all of your calculations and explain.  Use R, however, to check your work.

C. What is the 95‐percent confidence interval for years of education?  Provide a written interpretation explaining your answer.

As the director of the local Boys and Girls Club, you have claimed for years that membership in your club reduces juvenile delinquency. Now, a cynical member of your funding agency has demanded proof of your claim. Random samples of members and nonmembers are gathered and interviewed with respect to their involvement in delinquent activities. Each respondent is asked to enumerate the number of delinquent acts he/she has engaged in over the past year. The average number of admitted acts of delinquency are reported below. What can you tell the funding agency? Use an alpha of .01.

First, identify your (a) independent and (b) dependent variables.

Second, identify the (c) level of measurement for your independent variable and (d) the level of measurement for your dependent variable.

Third, (e) list out the steps of the 6 step traditional hypothesis test.

Fourth, (f) run a 6 step traditional hypothesis test.

(Conduct a 6 step traditional hypothesis test, find the p value).

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 60.0 kg and standard deviation σ = 8.0 kg. Suppose a doe that weighs less than 51 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)


(b) If the park has about 2500 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 60 does should be more than 57 kg. If the average weight is less than 57 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight

x

for a random sample of 60 does is less than 57 kg (assuming a healthy population)? (Round your answer to four decimal places.)


(d) Compute the probability that

x

< 61.2 kg for 60 does (assume a healthy population). (Round your answer to four decimal places.)


Suppose park rangers captured, weighed, and released 60 does in December, and the average weight was

x

= 61.2 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is below the mean, it is quite likely that the doe population is undernourished. Since the sample average is above the mean, it is quite likely that the doe population is undernourished.     Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished. Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.

According to the Bureau of Labor Statistics (as of May 2016), the mean annual wage for criminal justice and law enforcement professors is $67,040. The median annual wage is $59,590. Explain how each would be calculated and the advantages to using each over the other to characterize the typical annual salary. As a professor, which should I view as more accurate/appropriate? Explain your position.