Statistics Final Exam

Image 8 What is the correlation coefficient between tread depth and thousands of miles?

-0.976

Assume that event A occurs with probability 0.03 and event B occurs with probability 0.17. Assume that A and B are mutually exclusive events. What is the probability that both events occur?

0

Using the table from two questions earlier(Image 4), what is the probability that a randomly selected person is in poor health and not a current smoker? Round to 3 decimal places.

0.003

If events A and B are independent, the probability of A is 0.03, and the probability of B is 0.86, find P (A | B).

0.03

If events A and B are independent, the probability of A is 0.45, and the probability of B is 0.11, find P (A AND B). Do not round your answer.

0.0495

Using the table from the previous question(Image 4), what is the probability that a randomly selected person is a current smoker? Round to 3 decimal places.

0.094

According to the National Institute on Alcohol Abuse and Alcoholism, 45% of college students nationwide engage in binge drinking behavior. A college president wonders if the proportion of students enrolled at her college that binge drink is lower than the national proportion. Using a 90% confidence interval, what sample size is needed if she wants the margin of error to be less than 3 percentage points?

745

What is the approximate percentage of observations below the third quartile in a distribution? Hint: Think about the concept of quartiles.

75

Scores on a university exam are normally distributed with a mean of 77 and a standard deviation of 7. A score of at least 70 is required for a grade of at least C. Using the Empirical Rule, what percentage of students earned a grade of at least C?

84

The amount of time it takes Jolyn to wait in line at the bank is continuous and uniformly distributed between 7 and 12 minutes. What is the expected wait time for Jolyn?

9.5

Scores on a university exam are normally distributed with a mean of 77 and a standard deviation of 7. A score of at least 70 is required for a grade of at least C. Using the Empirical Rule, what percentage of students scored between 63 and 91?

95

Image 8 What percentage of the variation in tread depth is explained by the regression on miles?

95.3%

Which of the following shows independent events? Rolling a sum of 9 from the first two rolls of a standard die and a sum of 2 from the second two rolls Drawing a face card and then drawing a 6 without replacement from a standard deck of cards Rolling a 2 with a standard die and then rolling a sum less than 11 when counting the next roll Drawing an 8 and then drawing a 7 without replacement from a standard deck of cards

A

The average salary of all female workers at a large plant is $35,000. The average salary of all male workers at the plant is $41,000. If there are more female workers than male workers at the plant, then the average salary at the plant must be: smaller than $38,000 exactly $38,000 larger than $38,000

A

Which data set has the largest standard deviation? 23, 75, 77, 101 40, 47, 48, 57 34, 44, 55, 59 41, 45, 46, 51

A

Colleges often rely heavily on raising money for an annual fund to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's annual income is a good predictor of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. What is the response variable in these studies?

Amount he or she would be willing to donate

Colleges often rely heavily on raising money for an annual fund to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's annual income is a good predictor of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. Which variable goes on the y-axis of a scatterplot?

Amount he or she would be willing to donate

A national health survey of 1483 U.S. adults during 2014 revealed that 668 had never smoked cigarettes. Find a 95% large-sample confidence interval for the proportion of U.S. adults that had never smoked cigarettes. Enter the lower bound in the first answer blank and the upper bound in the second answer blank. Round your answers to the nearest thousandth.

Answer for blank #1: 0.425 Answer for blank #2: 0.476

The records of the 95 postal employees at a postal station in a large city showed that the average time these employees had worked for the postal service was 11.4 years with a standard deviation of 5.2 years. Assume that we know that the distribution of times U.S. postal service employees have spent with the postal service is approximately Normal. Find a 95% confidence interval. Enter the lower bound in the first answer blank and the upper bound in the second answer blank. Round your answers to the nearest hundredth.

Answer for blank #1: 10.34 Answer for blank #2: 12.46

The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC) are known to be Normally distributed with a standard deviation of 10. A simple random sample of 42 children from this population is taken and each is given the WISC. The mean of the 42 scores is 99.2. Find a 90% confidence interval. Enter the lower bound in the first answer blank and the upper bound in the second answer blank. Round your answers to the nearest hundredth.

Answer for blank #1: 96.66 Answer for blank #2: 101.74

You roll two six-sided dice, each numbered 1 through 6, and record the sum. Which of the following are in the sample space? 9 22 14 20 11 10

Anything between 2 and 12

List the conditions for the population proportion test.

random sample, at least 5 expected successes, and at least 5 expected failures

A college's professors are 45% male and 55% female. The college then randomly selects 9 of the male professors and 11 of the female professors to attend. Is this a simple random sample, stratified random sample, cluster sample, or convenience sample?

Stratified random sample

State the conditions for a confidence interval for two population means.

independent and random samples, known σ1 and σ2, two normal sampling distributions

Older men tend to have lower muscle density. Hence, the correlation between age and muscle density in older men must be negative.(T/F)

True

Using the histogram from two questions earlier, describe the shape of the distribution.(Image 1)

Unimodal and skewed right

List the conditions for the test of two population means.

two independent random samples, two normal sampling distributions

The amount of time it takes Jolyn to wait in line at the bank is continuous and uniformly distributed between 7 and 12 minutes. What is the probability that it takes Jolyn more than 11 minutes to wait?

0.2

A roulette wheel has 38 slots in which the ball can land. Two of the slots are green, 18 are red, and 18 are black. The ball is equally likely to land in any slot. The roulette wheel is going to be spun twice, and the outcomes of the two spins are independent. What is the probability that it lands on red on the first spin and black on the second? Round to three decimal places.

0.224

The amount of time it takes Jolyn to wait in line at the bank is continuous and uniformly distributed between 7 and 12 minutes. Given that Jolyn has been waiting for 8 minutes, what is the probability that it takes Jolyn more than 11 minutes to wait? Round your answer to two decimal places if needed.

0.25

Using the data from the previous question(Image 4), what is P (X < 2)?

0.268

A roulette wheel has 38 slots in which the ball can land. Two of the slots are green, 18 are red, and 18 are black. The ball is equally likely to land in any slot. The roulette wheel is going to be spun twice, and the outcomes of the two spins are independent. What is the probability that neither spin ends up on red? Round to three decimal places.

0.277

Using the table from 3 questions earlier(Image 4), answer the following. Given that a person is a current smoker, what is the probability that he/she is in very good health? Round to three decimal places.

0.285

What is the probability that a randomly selected person is in good health? Round to 3 decimal places(Image 4).

0.337

Using the table from 4 questions earlier(Image 4), answer the following. Given that a person is not a current smoker, what is the probability that he/she is in very good health? Round to three decimal places.

0.399

The amount of time it takes Jolyn to wait in line at the bank is continuous and uniformly distributed between 7 and 12 minutes. What is the probability that it takes between 9 and 11 minutes to wait?

0.4

Going back to the previous problem, if you weren't aware of the study done by the National Institute on Alcohol Abuse and Alcoholism, what value should you have used for the estimated proportion? According to the National Institute on Alcohol Abuse and Alcoholism, 45% of college students nationwide engage in binge drinking behavior. A college president wonders if the proportion of students enrolled at her college that binge drink is lower than the national proportion. Using a 90% confidence interval, what sample size is needed if she wants the margin of error to be less than 3 percentage points?

0.5

The score on the Wechsler Adult Intelligence Scale are approximately normal with μ=100 and σ=15. Using the standard normal table, what is the proportion of adults with scores above 99?

0.5279

Assume that event A occurs with probability 0.47 and event B occurs with probability 0.44. Assume that A and B are mutually exclusive events. What is the probability that B does not occur?

0.56

Assume that event A occurs with probability 0.39 and event B occurs with probability 0.26. Assume that A and B are mutually exclusive events. What is the probability that A or B occurs?

0.65

A basketball player makes 66% of his free throws. Let X represent the number of free throws made in three tries. The probability distribution for the number of free throws he makes in three attempts is summarized in the following table:(Image 5) What is the standard deviation of the number of free throws he will make? Round your answer to three decimal places.

0.820

The score on the Wechsler Adult Intelligence Scale are approximately normal with μ=100 and σ=15. Using the standard normal table, what is the proportion of adults with scores between 72 and 116?

0.8270

Colleges often rely heavily on raising money for an annual fund to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's annual income is a good predictor of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. Give an estimated value of the correlation.

0.93

The score on the Wechsler Adult Intelligence Scale are approximately normal with μ=100 and σ=15. Using the standard normal table, what is the proportion of adults with scores below 124?

0.9452

A basketball player makes 66% of his free throws. Let X represent the number of free throws made in three tries. The probability distribution for the number of free throws he makes in three attempts is summarized in the following table:(Image 5) What is the probability that he will make at least 1 free throw?

0.96

Using the data from the previous question, what is the five-number summary? Enter the values from least to greatest. 5, 3, 7, 6, 6, 2, 5, 3, 4, 7

2, 3, 5, 6, 7

The amount of time it takes Jolyn to wait in line at the bank is continuous and uniformly distributed between 7 and 12 minutes. What is the standard deviation of the wait time for Jolyn? Round to two decimal places.

1.44

A basketball player makes 66% of his free throws. Let X represent the number of free throws made in three tries. The probability distribution for the number of free throws he makes in three attempts is summarized in the following table:(Image 5) What is the expected value of the number of free throws he will make? Do not round.

1.978

You will be using this histogram on the next 5 questions. The histogram below shows the time spent by visitors at a museum browsing an exhibit on a Saturday. There were 300 visitors that day. The following histogram is of the data collected.(Image 1) Approximately how many visitors spent less than 55 minutes at the museum that day?

193

The 137 horses in a study on enteroliths, a type of stone in the gut, were housed either in a small paddock, large paddock, stall, or in a grass pasture. Based on the bar chart below(Image 3), what is the approximate percent of horses living in a pasture? Round to the nearest tenth of a percent, and do not write the % sign.

24.1

Image 8 What would be the predicted tread depth of a tire driven 10,000 miles? Do not round your answer.

286

A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. Previous research has shown the standard deviation to be 1.50. The researchers wish the margin of error to be no larger than 0.4 for a 90% confidence interval. What sample size is needed to accomplish this?

39

The following data will be used for the next 3 questions. A violin student records the number of hours she spends practicing during each of ten consecutive weeks. 5, 3, 7, 6, 6, 2, 5, 3, 4, 7 What is the mean? Enter an exact answer (i.e. no rounding).

4.8

A political party sends a mail survey to 1450 randomly selected registered voters in a community. The survey asks respondents to give an opinion about the job performance of the current President. Of the 1500 surveys sent out, 482 are returned, and of these, only 211 say they're satisfied with the President's job performance. What is the sample size?

482

Use the data from the previous question.(Image 1) Approximately what percentage of visitors spent more than 85 minutes at the museum that day? Round your answer to the nearest tenth of a percentage, and don't enter the % sign.

5.7

Which of the following will have a sampling distribution that is either Normal or approximately Normal? Select all correct answers. A sample of size 90 is selected from a distribution that is skewed right. A sample of size 80 is selected from a distribution with significant outliers. A sample of size 100 is selected from a distribution that is normal. A sample of size 20 is selected from a distribution that is normal. A sample of size 15 is selected from a distribution that is skewed left.

A, B, C, D

In the 2016 Olympics, Kévin Mayer of France finished first in the pole vault discipline of the decathlon with a height of 5.4 meters. The average height was 4.848 meters with a standard deviation of 0.300 meters. Ashton Eaton finished first in the long jump discipline of the decathlon with 7.94 meters. The average distance was 7.274 meters with a standard deviation of 0.318 meters. Which performance was more impressive?

Ashton Eaton had a more impressive performance since his Z-score was farther from 0 meaning it was farther from the average and thus more impressive.

A small math department has 30 students. It chooses students to attend a conference by picking a course and inviting every student enrolled in that course. Is this a simple random sample, stratified random sample, cluster sample, or convenience sample?

Cluster sample

List the conditions for the chi-square test.

Every expected value needs to be greater than 5.

A researcher finds the correlation between two variables is close to 0, so the two variables must be completely unrelated.(T/F)

False

Older children tend to be taller than younger children. Hence, the correlation between age and height in children must be negative.(T/F)

False

Taller people tend to be heavier than shorter people, so the correlation between height and weight must be negative.(T/F)

False

Using the table from 5 questions earlier(Image 4), are health rating and smoking independent? Explain.

Health rating and smoking are not independent, but dependent. Due to the large number of nonsmokers having health exceeding good in contrast to the number of smokers predominately having health that is good or below it is safe to say that one's health is in fact dependent upon whether they smoke or not. This is further proven by the fact that since overall health of nonsmokers is significantly better than that of a smoker, smoking is bad for you and lowers the status of your health.

A statistician wishing to test a hypothesis that students score more than 75% on the final exam in an introductory statistics course decides to randomly select 40 students in the class and have them take the exam early. The average score of the students on the exam was 77%. a. (4 points) State the hypotheses. You can use the HTML Editor to enter symbols including Greek letters. b. (4 points) If the p-value is 0.1029 and α=0.10, make a conclusion in a complete sentence related to the scenario.

Ho(Null): µ≤0.75 Ha(Alternative): µ>0.75 Due to the p-value being greater than alpha, we do not reject the null hypothesis since there is not sufficient evidence that students have an average score higher than 0.75 on this final exam.

The time (in number of days) until maturity of a certain variety of tomato plant is Normally distributed with a standard deviation of 2.4. I select a simple random sample of 15 plants of this variety and measure the time until maturity. The sample yields an average of 61.8 days. You read on the package of seeds that these tomatoes reach maturity, on average, in 60 days. You want to test to see if your seeds are reaching maturity later than expected. a. (4 points) State the hypotheses. You can use the HTML Editor to enter symbols including Greek letters. b. (4 points) If the p-value is 0.0018 and α=0.05, make a conclusion in a complete sentence related to the scenario.

Ho(Null): µ≤60 Ha(Alternative): µ>60 Due to alpha being greater than the p-value, the null hypothesis is rejected meaning that there is significant evidence proving that the seeds are reaching maturity later than expected.

A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, a random sample of 45 patients had an average systolic blood pressure of 142, with a standard deviation of 22. Is this sufficient evidence that the diet is effective in meeting the target? a. (4 points) State the hypotheses. You can use the HTML Editor to enter symbols including Greek letters. b. (4 points) If the p-value is 0.0094 and α=0.01, make a conclusion in a complete sentence related to the scenario.

Ho(Null): µ≥150 Ha(Alternative): µ<150 Due to alpha being greater than the p-value, the null hypothesis is rejected meaning that there is significant evidence proving that the diet is effective in meeting its target.

Using the histogram from 4 questions earlier(Image 1), would it be better to use mean and standard deviation OR a five-number summary to describe this data? Briefly explain your reasoning.

It would be best to use a five-number summary because, there are outliers in this histogram which demerits the use of mean and standard deviation which rely on a lack of outliers. a five-number summary would be best used here since it includes median which can accurately find the center when there are outliers, additionally, using Q1 and Q3 you can find the IQR which can be used to accurately determine if there are outliers in play by cross-referencing that with the maximum and minimum, which is also shown in the five-number summary.

State the conditions for a large-sample confidence interval for a population proportion.

More than 5 successes and 5 failures.

A company has three divisions and three conference rooms for meetings. To keep track of the use of their facilities, for each meeting held in the company, they record which division is holding the meeting, the room for the meeting, and the length of time for the meeting. Is the division qualitative or quantitative? Is the room qualitative or quantitative? Is the length of time qualitative or quantitative?

Qualitative, Qualitative, Quantitative

Given the data below(Image 2), complete parts (a) and (b) on a sheet of paper that you will upload to the Test 1 Dropbox. What you type in the answer box will not be graded. (a) Construct a stem-and-leaf plot with a stem unit of 10 and a leaf unit of 1 (b) Construct a histogram using classes of size 10 with the first class being 10-19.

Question 25 Test 1, but on the stem and leaf plot, the numbers need to be equally spaced

5, 3, 7, 6, 6, 2, 5, 3, 4, 7 Using the same data as the previous two questions, construct a box-and-whiskers plot. What you type in this answer box will not be graded.

Question 5 image from document with pics from test 1

State the conditions for a confidence interval for a population mean with a known population standard deviation.

Random sampling and normal distribution.

A college randomly selects 20 professors to attend a conference. Is this a simple random sample, stratified random sample, cluster sample, or convenience sample?

Simple random sample

Image 8 In this study, which variable is the explanatory variable?

The distance driven

Colleges often rely heavily on raising money for an annual fund to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's annual income is a good predictor of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. What is the explanatory variable in these studies?

The graduate's annual income

A 1992 Roper poll found that 22% of Americans say that the Holocaust may not have happened. The actual question asked in the poll was, "Does it seem possible or impossible to you that the Nazi extermination of the Jews never happened?" Explain why the results cannot be trusted.

The main issue is that the survey question is confusing and may have caused participants to answer the opposite of what they intended.

A political party sends a mail survey to 1450 randomly selected registered voters in a community. The survey asks respondents to give an opinion about the job performance of the current President. Of the 1500 surveys sent out, 482 are returned, and of these, only 211 say they're satisfied with the President's job performance. What should be the population of this study? Be specific.

The population would be registered voters in that specific community.

To assess the opinion of students at The Ohio State University about campus safety, a reporter for the student newspaper interviews 25 students she meets walking on the campus late at night who are willing to give their opinion. Explain why the results cannot be trusted.

The results cannot be trusted because there is clear sampling bias present in the survey. The interview takes place at the campus late at night which is generally thought of as an unsafe setting, leading to the possibility that since people are out late at night they assume that their campus is safe since they are willing to walk around there during the time of night when there is less safety than during day. Additionally, this survey used convenience sampling which generally isn't as trusted as other types of sampling.

The population is Normally distributed. A random sample of 142 individuals has a mean of 19.9 and a standard deviation of 4.48. The hypotheses are:H0: μ = 20.5Ha: μ ≠ 20.5 a. Identify whether the test statistic is z or t, and calculate it. b. Find the p-value.

The test statistic is t which equals -1.60. The p-value is 0.10 is less than p which is less than 0.20.

The population is Normally distributed. A random sample of 29 individuals has a mean of 500 and a standard deviation of 20. The hypotheses are:H0: μ = 510Ha: μ < 510 a. Identify whether the test statistic is z or t, and calculate it. b. Find the p-value.

The test statistic is t which equals -2.69. The p-value is 0.005 is less than p which is less than 0.01.

The population is Normally distributed with a standard deviation of 5.8. A random sample of 58 individuals has a mean of 47.2. The hypotheses are:H0: μ = 48Ha: μ ≠ 48 a. Identify whether the test statistic is z or t, and calculate it. b. Find the p-value.

The test statistic is z and it equals -1.05. The p-value is 0.2938.

During the 1936 presidential election between Franklin D. Roosevelt and Alf Landon, the Literary Digest received 2.3 million mail-in surveys that it used to predict the results: a landslide in favor of Landon. Explain why the results cannot be trusted.

These results cannot be trusted because the people who sent in the survey are all subscribed to the Literary Digest which could generally have a biased view of the presidential election and not be completely unbiased in their reporting. Due to this, it would lead to the readers of the Literary Digest being a biased sample and more likely to choose one candidate over the other.

Veterinarians often use nonsteroidal anti-inflammatory drugs (NSAIDs) to treat lameness in horses. A group of veterinary researchers wanted to find out how widespread the practice was in the United States. They obtained a list of all veterinarians treating horses. They sent questionnaires to all the veterinarians on the list. Only 40% of them returned the questionnaire. Explain why the results cannot be trusted. (STUDY TYPES OF BIAS)

These survey results cannot be trusted because they contain voluntary bias meaning that people chose to fill them out and some didn't. Often times in these type of scenarios the majority of people filling out these surveys feel strongly about the issue whatever their stance may be. This leads to the population not accurately being represented since the people who don't care as much about the issue aren't surveyed since it heavily relies on volunteers.

A political party sends a mail survey to 1450 randomly selected registered voters in a community. The survey asks respondents to give an opinion about the job performance of the current President. Of the 1500 surveys sent out, 482 are returned, and of these, only 211 say they're satisfied with the President's job performance. What is a reason the survey results cannot be trusted? (STUDY TYPES OF BIAS)

These survey results cannot be trusted because they contain voluntary bias meaning that people chose to fill them out. Often times in these type of scenarios the far majority of people filling out these surveys feel strongly about the issue whatever their stance may be. This leads to the population not accurately being represented since the people who don't care as much about the issue aren't surveyed since it heavily relies on volunteers.

Using your answer for the previous question, write the confidence interval in a complete sentence related to the scenario. (96.66, 101.74)

We are 90% confident that this certain population on the WISC will have an average score between 99.66 and 101.74.

Using your answer for the previous question, write the confidence interval in a complete sentence related to the scenario. (0.425, 0.476)

We are 95% confident that the proportion of U.S. adults who have never smoked a cigarette is between 0.425 and 0.476.

Image 8 Can we use the least-squares regression line to predict the tread depth for any number of miles? If not, for how many thousands of miles would you be comfortable using the regression line?

We can not use the least-squares regression line to predict the tread depth for any number of miles since the sample size does not include every possible value and also because the line eventually goes into the negative for tread depth which is not possible. I would be comfortable using the regression line to predict the tread depth for up to 50 thousand miles since that is the furthest the linear regression line goes before it starts giving negative tread depth(y-axis does not have 0), which again, is not possible.

Using your answer for the previous question, write the confidence interval in a complete sentence related to the scenario. (10.34, 12.46)

We can say with 95% confidence that the average amount of time a postal employee has worked for the postal service is between 10.34 years and 12.46 years.

Based purely on the histogram (i.e. no calculations necessary), is there an outlier?(Image 1) Briefly explain why or why not.

Yes, 145-155, is an outlier. The substantial number of visitors are to the left of the outlier by a sizeable margin. Due to this large gap, 145-155 can be thought of as an outlier.

A veterinary study of horses looked at water sources for horses, and the investigators found that horses received water from a well, city water, or a stream. The investigators wanted to know if horses are equally likely to get water from each of those three sources. a. What are the appropriate hypotheses? b. If the p-value is 0.0287 and α is 0.10, give a conclusion in a complete sentence related to the scenario.

a. Ho: It is equally likely for horses to get water from any of the 3 sources Ha: It is not equally likely for horses to get water from any of the 3 sources b. Due to the p-value being less than the significance level or a, we reject the null hypothesis and there is sufficient evidence to suggest that horses are not equally likely to get water from those 3 sources.

In the United States, there has historically been a strong relationship between smoking and education, with well-educated people less likely to smoke. To examine whether this pattern has changed, a sample of 468 men was selected at random from those who had visited a health center for a routine check-up over the course of the past year. Education was classified into three categories corresponding to the highest level of education achieved, and smoking status was classified into four categories. A test was done to see if education and smoking status are dependent. a. What are the appropriate hypotheses? b. If the p-value is 0.0370 and α is 0.05, give a conclusion in a complete sentence related to the scenario.

a. Ho: The level of education of someone and their smoking status are independent Ha: The level of education of someone and their smoking status are dependent b. Due to the p-value being less than the significance level or a, we reject the null hypothesis and there is sufficient evidence to suggest that education, and smoking status are dependent.

The American Veterinary Medical Association conducted a survey of veterinary clinics to estimate the proportion that do not treat large animals (cows, horses, etc.). Typically, 70% of the veterinary clinics in the world do not treat large animals. You wish to test whether American veterinary clinics are more likely to not provide this service. a. What are the appropriate hypotheses? b. If the p-value is 0.2097 and α is 0.01, give a conclusion in a complete sentence related to the scenario.

a. Ho: p=0.7 Ha: p>0.7 b. Due to the p-value being greater than the significance level or a, we do not reject the null hypothesis and there is insufficient evidence to suggest that more than 70% of the veterinary clinics in America do not treat large animals.

DDT is a pesticide banned in the United States for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not exposed. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. Let μ1 be the mean nerve sensitivity for rats poisoned with DDT. Let μ2 be the mean nerve sensitivity for rats not poisoned with DDT. a. What are the appropriate hypotheses? b. If the p-value is 0.0084 and α is 0.01, give a conclusion in a complete sentence related to the scenario.

a. Ho: µ1=µ2 Ha: µ1>µ2 b. Due to the p-value being less than the significance level or a, we reject the null hypothesis and there is sufficient evidence to suggest that DDT increases nerve sensitivity in rats.

The amount of milk sold each day by a grocery store varies according to the Normal distribution with mean 120 gallons and standard deviation 9 gallons. a. (5 points) On a randomly-selected day, what is the probability that the grocery store sells at least 128 gallons? Round your answer to 3 decimal places. b. (5 points) Over a span of 10 days (assuming the randomness requirement is not violated), what is the probability that the grocery store sells an average of at least 128 gallons? Round your answer to 4 decimal places, if needed.

a. 0.187 b. 0.0025

Image 6 a. Identify the test statistic as z, t, or χ2, and evaluate it. b. Make a conclusion using either the critical value or p-value approach with α = 0.05.

a. The test statistic is X^2 and X^2=0.6138 b. Due to the critical value being 3.84 and greater than the test statistic which is 0.6138, we do not reject the null hypothesis which means that there is insufficient evidence that the genders of the child and the parent carrying it are dependent.

Image 7 a. Identify the test statistic as z, t, or χ2, and evaluate it. b. Find the p-value.

a. The test statistic is t and t=1.847 b. The p-value is between 0.025 and 0.05

Given the hypotheses H0: p = 0.10 Ha: p ≠ 0.10 and a random sample with 12 successes out of 180 individuals, do the following. a. Identify the test statistic as z, t, or χ2, and evaluate it. b. Find the p-value.

a. The test statistic is z and z= -1.49 b. The p-value is 0.1362