correct answers no copying from other sites i will have follow up questions on each question

FOR QUESTION 20 PLEASE USE THE SCENARIO BELOW

My niece wants to get a beaver as a pet. My sister said she couldn't because they're much bigger than cats. So, naturally, my niece weighed thirty-six randomly selected beavers (in kilograms, of course), having an average weight of 3.8 kg and standard deviation of 0.2 kg. The average weight of a house cat is 4 kg. Of course 3.8 kg is less than 4 kg, but can we statistically conclude that beavers are lighter, on average, than house cats? Let's conduct a hypothesis test to find out. This might help my niece convince my sister.

20. Identify the most appropriate part of the context for each of the following.

A. The cases/individuals/units of observation

B. The population of interest

C. The parameter of interest

D. The sample statistic

E. The sample

21. Match the following symbols to what they typically represent.

mu

a. sample mean

b. population mean

c. population standard deviation

d. population correlation

e. sample standard deviation

f. sample proportion

g. population proportion

h. sample correlation

xbar

a. sample mean

b. population mean

c. population standard deviation

d. population correlation

e. sample standard deviation

f. sample proportion

g. population proportion

h. sample correlation

p

a. sample mean

b. population mean

c. population standard deviation

d. population correlation

e. sample standard deviation

f. sample proportion

g. population proportion

h. sample correlation

phat

a. sample mean

b. population mean

c. population standard deviation

d. population correlation

e. sample standard deviation

f. sample proportion

g. population proportion

h. sample correlation

sigma

a. sample mean

b. population mean

c. population standard deviation

d. population correlation

e. sample standard deviation

f. sample proportion

g. population proportion

h. sample correlation

s

a. sample mean

b. population mean

c. population standard deviation

d. population correlation

e. sample standard deviation

f. sample proportion

g. population proportion

h. sample correlation

rho

a. sample mean

b. population mean

c. population standard deviation

d. population correlation

e. sample standard deviation

f. sample proportion

g. population proportion

h. sample correlation

r

a. sample mean

b. population mean

c. population standard deviation

d. population correlation

e. sample standard deviation

f. sample proportion

g. population proportion

h. sample correlation

22. In the context of my niece getting a beaver as a pet, The null (H0) and alternative (H1,HA,Ha) hypotheses would compare the parameter of interest to...

a. the center of the normal distribution, 0

b. the standard deviation, 0.2 kg

c. the mean weight of cats, 4 kg

d. the average weight of the weighed beavers, 3.8 kg

23. The alternative hypothesis would be of the form...

a. parameter > number

b. parameter < number

c. parameter number

d. parameter = number

24. Suppose my niece completed the hypothesis test and failed to reject the null hypothesis. Which type of statistical error might she be making?

a. Type I - rejecting a true null

b. Type II - failing to reject a false null

25. What are some of the possible consequences in making the two types of statistical errors in this context? Be very clear in distinguishing the types of errors and their consequences.

26. My niece found a p-value smaller than 0.0001. What would her statistical conclusion be if the significance level was =10%=0.10?

a. Reject the null hypothesis

b. Accept the null hypothesis

c. Fail to reject the null hypothesis

27. Reword this conclusion in the context of the problem and, in particular, what this means about the likelihood of my niece getting a new pet beaver, assuming that my sister was honest in her objection based on their average weight.

28. To further support her claim, my niece found the 70% confidence interval for the true mean weight of beavers to be (3.76, 3.84) kg.

(a) Interpret the confidence interval statistically.

(b) Provide a less wordy, real-world interpretation of the confidence interval.

(c) Discuss how the confidence interval would change if my niece using a greater confidence level (say, 90%, 95%, or 99%).

A study is performed involving two methods for removing harmful bacteria in 350 lakes in Florida. The lakes were treated randomly using one of two methods. Specifically, 150 were treated using Method A and 200 were treated using Method B. A total of 250 of the 350 lakes were bacteria-free after treatment, 95 from the Method A group and 155 from the Method B group. A significance test was performed for the following hypotheses and resulted in a p-value of 0.0018: H₀: Bacteria removal rates are the same for Method A and B H_a: Method B has a higher bacteria removal rate Part A: Interpret the p-value in terms of the context. Part B: Using a significance level of = 0.05, what can you conclude from the context of this study? Part C: Based on your conclusion in part B, which type of errorType I or Type IIcould have been made? What is one potential consequence of this error?

2.

(06.04 MC) A recent study of high school students shows the percentage of females and males who have at LEAST one notation in their school record for inappropriate behavior. A simple random sample of high school students was interviewed. The students were asked whether they had a notation for inappropriate behavior in their school record. Of the 100 females, 21 answered yes, as did 145 of the 400 males. Part A: Construct and interpret a 99% confidence interval for the difference in population proportions of females and males who have at LEAST one notation for inappropriate behavior. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain.

For a cooking oil company, the price they are paid for coconuts in large shipments is based on the amount of coconut extract from the load.Therefore, there is a need to determine the amount of coconut extract in the whole load prior to extraction. A sample of n coconut can be taken and find y₁, . . . , y_n ,the amount of coconut extract in these coconuts.

Nis hard to get in this case because N is hard to count. How can the total amount of coconut extract from a load shipment be measured? Using the total weight would be a good idea and easy to obtain. The relationship between the weight of the load and the weight of the coconut extract one obtains can be used. As it turns out, 15 coconuts selected by simple random sampling were weighed and also extracted. The total weight of the coconut shipment was found to be 900 kg.Given these results (below):

3.

(06.01, 06.02 MC) At a Clover City Council meeting, a plan to fund more sign language programs was presented. The reasoning behind the request was that less than 25% of parents with hearing-impaired children have the ability to pass a sign-language exam. If this is true, the council will agree to fund more programs for these parents. The council decides to take a 175-person volunteer sample of parents in Clover City that have children with auditory issues and conduct a significance test for H0: p = 0.25 and Ha: p < 0.25, where p is the proportion of these parents that can pass the sign language exam. They will perform the significance test at a significance level of = 0.05 for the hypotheses. Part A: Describe a Type II error that could occur. What impact could this error have on the situation? (3 points) Part B: Out of the 175 volunteer parents of children with hearing problems, 54 passed, resulting in a p-value of 0.96. What can you conclude from this p-value given the data of the 175 parents is sufficient to perform a significance test for the hypotheses? Part C: What possible defect in the study can you find in Part B? Explain.

4.

(06.01 LC) A test of H₀: p = 0.4 versus H_a: p > 0.4 has the test statistic z = 2.52. Part A: What conclusion can you draw at the 5% significance level? At the 1% significance level? Part B: If the alternative hypothesis is H_a: p 0.4, what conclusion can you draw at the 5% significance level? At the 1% significance level?

5.

(06.05 HC) A survey of 340 randomly chosen US adults found that 60% of the 150 men and 50% of the 190 women ran a five-kilometer race during the past month. Do these data provide statistical evidence at the = 0.05 level that women are less likely than men to run a five-kilometer race? Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (10 points)