An economist with the Liquor, Hospitality and Miscellaneous Workers' Union collected data on the weekly salaries of workers in the hospitality industry in Cairns and Townsville. The union believed that the weekly salaries of employees in Cairns were higher and they were mounting a case for the equalisation of salaries between the northern cities. The researcher took samples of size 30 and 37 in Cairns and Townsville, respectively, and found that the average and standard deviation of the weekly salaries were $585.43 and $38.72 respectively in Townsville, and $616.19 and $29.13 in Cairns. Use Cairns minus Townsville.

1. Determine a point estimate for the value of the difference in average weekly salary between the two groups (in dollars to 2 decimal places).

2. Calculate the standard error for the difference between the means assuming that the workers' salaries in both locations are normally distributed and have the same population variance (in dollars to 2 decimal places).

3. Use Kaddstat to determine a 95% confidence interval for the difference between the average weekly salaries in Cairns and Townsville.

a. lower limit

b. upper limit (in dollars to 2 decimal places)

We have to randomly select 2 students for an award from a group of 5 equally deserving students. Of the five students two are female and three are male.Event C as selecting at least one female. Define event D as awarding only one male, what is the probability of event D? P(C U D) 8. P(C ∩ D) Are C and D disjoint?

Explain in detail using sample space if possible. And pls if you use symbols like this: a) D = {one male and one female} P(D) = 2C1 * 3C1 / 5C2 = 2 * 3 / 10 = 0.6 please explain what C is? what does 2C1 ,means?

1.The US justice system considers an accused person innocent until proven guilty and there has to be proof beyond a reasonable doubt to convict the accused. In recent years, several individuals have been released from prison because new DNA tests proved them innocent. When the court originally convicted them (falsely as it turns out): (check all that apply)

2.In hypothesis testing, a Type 2 error occurs when (check all that apply)

3.Null and alternative hypotheses are statements about: (check all that apply)

A researcher intended to investigate the potential association between Age Group and Smoking Status. He collected data from 575 participants. The data was summarized in Table 2. Was the data in support of a statistically significant association between Age Group and Smoking Status? The significance level was 0.05. How do you determine the expected levels in the chi test?

Table . Age Group and Smoking Status

Air traffic controllers perform the vital function of regulating the traffic of passenger planes. Frequently, air traffic controllers work long hours with little sleep. Researchers wanted to test their ability to make basic decisions as they become increasingly sleep deprived. To test their abilities, a sample of 6 air traffic controllers is selected and given a decision-making skills test following 12-hour, 24-hour, and 48-hour sleep deprivation. Higher scores indicate better decision-making skills. The table lists the hypothetical results of this study.

(a) Complete the F-table. (Round your answers to two decimal places.)

2.) Seasonal affective disorder (SAD) is a type of depression during seasons with less daylight (e.g., winter months). One therapy for SAD is phototherapy, which is increased exposure to light used to improve mood. A researcher tests this therapy by exposing a sample of SAD patients to different intensities of light (low, medium, high) in a light box, either in the morning or at night (these are the times thought to be most effective for light therapy). All participants rated their mood following this therapy on a scale from 1 (poor mood) to 9 (improved mood). The hypothetical results are given in the following table.

(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Round your answers to two decimal places. Assume experimentwise alpha equal to 0.05.)

Compute Tukey's HSD to analyze the significant main effect.

The critical value is  for each pairwise comparison.

Summarize the results for this test using APA format.

4) A recent Harris Poll on green behavior showed that 25% of adults often purchased used items instead of new ones. If a random sample of 5 adults is used, what is the probability that no more than 4 of the sampled adults purchase used items instead of new ones? Round to the nearest thousandth.

5) In order to answer the question "What percentage of hospitals provide at least some charity care?", the following problem is based on information taken from State Health Care Data: Utilization, Spending, and Characteristics (American Medical Association). Based on a random sample of hospital reports from eastern states, the following information was obtained (units in percentage of hospitals providing at least some charity care):

57.1 56.2 53.0 66.1 59.0 64.7 70.1 64.7 53.5 78.2

What is the mean for this data? Round to the nearest hundredth.

6) In order to answer the question "What percentage of hospitals provide at least some charity care?", the following problem is based on information taken from State Health Care Data: Utilization, Spending, and Characteristics (American Medical Association). Based on a random sample of hospital reports from eastern states, the following information was obtained (units in percentage of hospitals providing at least some charity care):

57.1 56.2 53.0 66.1 59.0 64.7 70.1 64.7 53.5 78.2

What is the standard deviation for this data? Round to the nearest hundredth

A quality controller at a beverage manufacturer is concerned that a bottling machine is under-filling (an opaque container) that is supposed to contain 1000 mL of fluid. A random sample of 20 containers is therefore taken and the volume in each recorded in the file STA201 201960 Assn Bottles.xlsx. In researching the problem the quality controller sees a statement in the machine’s manual that “volumes dispensed by the machine will follow a normal distribution”. (a) Based on the information provided, write down the null and alternate hypothesis that the quality controller should employ to test this concern. (b) Say why the statement in the manual is important to this analysis and then write down the name of the test to be employed. (c) Write down the decision rule in terms of a test statistic and give the corresponding decision rule using a p value. Note: Use a 5% level of significance for the test. (d) Calculate the value of the test statistic manually. (e) State whether you reject the null hypotheses or otherwise, justify your decision and then draw a conclusion that answers the original question.

A marketing study was conducted to assess the new bottle design of a popular soft drink. Sixty randomly selected shoppers participated and rated the new design. The data are given below:

34 33 33 29 26 33 28 25 32 33
32 25 27 33 22 27 32 33 32 29
24 30 20 34 31 32 30 35 33 31
32 28 30 31 31 33 29 27 34 31
31 28 33 31 32 28 26 29 32 34
32 30 34 32 30 30 32 31 29 33

a. Explain why we need to construct a frequency distribution and histogram for this data set.
b. Construct a relative frequency distribution and a percent frequency distribution for the bottle design ratings.
c. Construct a cumulative frequency distribution and cumulative percent frequency distribution.

A box contains 4 tickets. 1 ticket is numbered 0, 1 ticket is numbered 1, and 2 tickets are numbered 2. Suppose n draws with replacement are made from this box. Let Sn be the sum of the numbers drawn. a) Approximate the probability P(S100=100)

(a). Roll a die until you get your 17th ace. Let T be the number of rolls you need to get that 17th ace.

Find E(T) and var(T).

(b). Let Y = T-17 = "number of non-aces rolled to get your 17th ace". Y is called a "negative binomial" random variable, with parameters r=17 and p= 1/6.

Find E(Y) and var(Y).

(c). Find the approximate value of P{ T > 120 }

This variance can also be found in a tedious way (but not requiring any cleverness) using the "moment-generating function" of X given by m(t) = E[ e^(tX)]. Look it up if you have OCD.

A box has 11 parts of which 4 are defective and 7 acceptable. 2 parts are chosen at random without replacement. Find the probability that:

a) both parts are defective.

b) both parts are acceptable.

c) only one part is defective.

An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola.

Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use

α = 0.05.)

State the relevant hypotheses. (Use μ₁ for the strawberry drink and μ₂ for the cola.)

H₀: μ₁ − μ₂ = 0
H_a: μ₁ − μ₂ > 0H₀: μ₁ − μ₂ = 0
H_a: μ₁ − μ₂ ≠ 0    H₀: μ₁ − μ₂ = 0
H_a: μ₁ − μ₂ ≥ 0H₀: μ₁ − μ₂ = 0
H_a: μ₁ − μ₂ < 0

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

State the conclusion in the problem context.

Reject H₀. The data suggests that cola has a higher average compression strength than the strawberry drink.

Reject H₀. The data does not suggest that cola has a higher average compression strength than the strawberry drink.   

Fail to reject H₀. The data suggests that cola has a higher average compression strength than the strawberry drink.

Fail to reject H₀. The data does not suggest that cola has a higher average compression strength than the strawberry drink.

What assumptions are necessary for your analysis?

The distributions of compression strengths are the same.

The distributions of compression strengths have equal variances.    

The distributions of compression strengths are approximately normal.

The distributions of compression strengths have equal means.

Ken has a coin that has probability 1/5 of landing Heads.

   Mary has a coin that has probability 1/3 of landing Heads.

   They toss their coins simultaneously, repeatedly.

Let X be the number of tosses until Ken gets his first Heads.

Let Y be the number of tosses until Mary gets her first Heads. Find:

Let U = min(X,Y) and V = max(X,Y)

(d) For k = 1, 2, 3,... , find a formula for P(U = k).

(e) For k = 1, 2, 3,... , find a formula for P(V > k). HINT: Inclusion-Exclusion.

A beef cattle nutritionist wants to compare the birth weights of calves from cows that receive two different diets during gestation. He therefore selects 16 pairs of cows, where the cows within each pair have similar characteristics. One cow within each pair is randomly assigned to diet 1, while the other cow in the pair is assigned to diet 2. He obtains the following results:

     Mean difference in birth weights of the pairs of calves = 10 lb

     Standard deviation of the difference in birth weights of the pairs = 8.0 lb

Construct a 95% confidence interval for the true mean difference in birth weights of the calves from cows receiving diet 1 vs. diet 2.

Group of answer choices

(5.738 lb, 14.262 lb)

(6.08 lb, 13.92 lb)

(6.606 lb, 13.394 lb)

(4.97635 lb, 17.02365 lb)

A procurement specialist has purchased 25 resistors from Vendor 1 and 35 resistors from Vendor 2. Each resistor’s resistance was measured and reported in Problem 4 spreadsheet of Homework 2.xlsx. You want to compare mean performance. Use R, and draw conclusions with 0.05 significance. a. First perform the appropriate test to determine whether to assume equal or unequal dispersions of resistance for the two vendors. b. Based on your answer in part a, compare mean performance of the vendors with the appropriate ? test.