Sara is a big hip-hop music fan. Her friend Matt is a big rap music fan. They each have a huge library of songs in their digital music libraries. They each randomly sample 50 songs from their libraries and record the lengths of the songs selected. The average of the selected hip-hop songs was

x₁ = 240

seconds with a sample standard deviation of 5 seconds. The average of the selected rap songs was

x₂ = 265

seconds with a sample standard deviation of 8 seconds. They would like to know if the average length of hip-hop songs is different than the average length of rap songs.

(a)

What are the appropriate null and alternative hypotheses for this test?

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ < 0

H_a: μ₁ − μ₂ > 0

(b)

Calculate the test statistic. (Round your answer to two decimal places.)

(c)

Assume for purposes of this study, the degrees of freedom are 80. At a 5% significance level, what is the critical value for the test? (Round your answer to two decimal places. Just give the value of the critical value, no negative or positive sign)

A study was conducted to see whether two types of cars, A and B, took the same time to parallel park. Seven drivers were randomly obtained and the time required for each of them to parallel park (in seconds) each of the 2 cars was measured. The results are listed below in order of driver (e.g. the first listing for A and B are driver 1; the second listing driver 2; etc.) Car A: 19, 21.8, 16.8, 24.2, 22, 34.7, 23.8 Car B: 17.8, 20.2, 16.2, 41.4, 21.4, 28.4, 22.7

A. Explain why this is a paired test and not a two sample test.

B. Test whether the there is a difference in mean parallel parking time of the two cars at a 0.05 level of significance. Include the hypotheses, the test statistic, the p-value, test decision and conclusion in the context of the problem.

C. Do you believe the test results are valid? Explain.

D. What test decision error could you have made and provide an explanation of this error in context of the problem. E. Include a copy of your R-code and test output.

1) Researchers in South Africa were interested in prevalence of HIV-related behaviors and infection in the population. They administered a survey of 500 men and women who came for health care at a hospital clinic in Johannesburg. At the same time, all subjects were tested for HIV status. Prevalence of HIV was higher in men than in women. Men were also more likely to use IV drugs and to engage in sex with multiple sex partners. What type of study design is this?

2)

Investigators interested in whether maternal-fetal sharing of HLA genes was associated with preeclampsia identified recent births from state birth certificate files. They selected all women whose birth certificate indicated preeclampsia in pregnancy and a random sample of women for whom preeclampsia was not indicated on the birth certificate. After confirming preeclampsia status in medical records, a total of 250 women with preeclampsia and a similar number of women without preeclampsia were enrolled. All women provided buccal cell samples from themselves and their babies for HLA-typing. Maternal-fetal sharing was more common among women with preeclampsia than women without preeclampsia. What type of study design is this?

In a randomly selected sample of 500 registered voters in a community, 120 individuals say that they plan to vote for Candidate Y in the upcoming election.

(a) Find the sample proportion planning to vote for Candidate Y. (Round your answer to two decimal places.)


(b) Calculate the standard error of the sample proportion. (Round your answer to three decimal places.)


(c) Find a 95% confidence interval for the proportion of the registered voter population who plan to vote for Candidate Y. (Round your answers to three decimal places.)
to  

(d) Find a 98% confidence interval for the proportion of the registered voter population who plan to vote for Candidate Y. (Round your answers to three decimal places.)
to

JOBCO produces two products on two machines. A unit of product 1 requires 2 hours on machine 1 and 1 hour on machine 2. For product 2, a unit requires 1 hour on machine 1 and 3 hours on machine 2. The revenues per unit of products 1 and 2 are $30 and $20, respectively. The total daily processing time available for each machine is 8 hours. Letting x1 and x2 represent the daily number of units of products 1 and 2, respectively, the LP model is given as

max z=30x1+20x2

s.t.

2x1+x2 ≤8

x1+3x2 ≤8

x1,x2 ≥ 0

equation to be solved using simplex method.

If JOBCO can increase the capacity of both machines, which machine should receive higher priority?

I need it to be solved in details using shadow price and delta in the right hand side.

What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data.

(a) Find Σx, Σy, Σx², Σy², Σxy, and r. (Round r to three decimal places.)

(b) Use a 1% level of significance to test the claim that ρ < 0. (Round your answers to two decimal places.)

Conclusion

Reject the null hypothesis. There is sufficient evidence that ρ < 0.Reject the null hypothesis. There is insufficient evidence that ρ < 0.    Fail to reject the null hypothesis. There is insufficient evidence that ρ < 0.Fail to reject the null hypothesis. There is sufficient evidence that ρ < 0.

(c) Find S_e, a, and b. (Round your answers to five decimal places.)

(d) Find the predicted optimal time in hours for a dive depth of x = 20 meters. (Round your answer to two decimal places.)
hr

(e) Find an 80% confidence interval for y when x = 20 meters. (Round your answers to two decimal places.)

(f) Use a 1% level of significance to test the claim that β < 0. (Round your answers to two decimal places.)

Conclusion

Fail to reject the null hypothesis. There is insufficient evidence that β < 0.Fail to reject the null hypothesis. There is sufficient evidence that β < 0.    Reject the null hypothesis. There is insufficient evidence that β < 0.Reject the null hypothesis. There is sufficient evidence that β < 0.

(g) Find a 90% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.)

Interpretation

For a 1 meter increase in depth, the optimal time decreases by an amount that falls within the confidence interval.For a 1 meter increase in depth, the optimal time decreases by an amount that falls outside the confidence interval.    For a 1 meter increase in depth, the optimal time increases by an amount that falls within the confidence interval.For a 1 meter increase in depth, the optimal time increases by an amount that falls outside the confidence interval.

A subject is presented with three cups, two of which contain the same brand of cola and one of which contains a different brand. The subject is to identify which one of the three cups contains a different brand of cola than the other two. We wish to determine if the subject will perform better than randomly guessing over 75 trials. (Use 4 decimal places for all calculations)

a) H_0 is pi =

H_a is pi >   

b) n*pi =  and n*(1-pi) =  . Is the CLT valid? (yes/no)

Suppose the subject guessed correctly 31 times.

c) Calculate the test statistic =  (this answer only 2 decimal places)

d) Calculate the p-value =

e) If alpha = .05, would you reject o fail to reject the null?

The number of robocalls received by a given household in twelve randomly selected weeks results in the following data set: {9, 7, 2, 9, 4, 8, 4, 10, 15, 10, 20, 8}. Use this to find the 90% confidence interval estimate of the mean number of calls received per week. Use a T-interval.

Select one:

a. (5.72, 11.94)

b. (6.06, 11.60)

c. (6.30, 11.37)

d. (6.51, 11.16)

e. (4.44. 13.22)

f. (6.61, 11.06)

A sample is selected to find a 90% confidence interval for the average starting salary. Here are the sample statistics: n = 31, x ̄ = $43, 780, s = $1, 600.

a). Find the t− score used in the calculation of the confidence interval.

b). Build a 90% confidence interval for the mean starting salary.

c). Based on the result of part b), could we make a conclusion that the mean staring salary is below $45, 000? Explain your reason.

Right after the poll stations are closed at 17:00, a political candidate receives the
information that out of the 50 people interviewed her approval “count” is 24. As a statistics
lover, she immediately tests the null hypothesis that her population approval rate is less than
or equal 0.50 against its respective alternative, at the 5% level of statistical significance. What
is the conclusion of this test? Suppose in every consecutive 15 minutes, number of people
interviewed increases by 5 and approval count increases by 4. Find the earliest time, HH:MM,
that she can declare her victory based on her tests of hypotheses. Note that a formal
statistical/algebraic solution is expected with proper terminology and notation.

3. Suppose that you are working for a watch company studying the average wrist sizes of people in the population of the United States.

(a) If you are told that we know from previous studies that the standard deviation in women’s wrist sizes is 0.5 inches, and from a random sample of 20 women, the sample mean wrist size was 7.2 inches, create a 95% confidence interval for the true mean wrist size.

(b) Your boss comes back and tells you that they found out that the sample actually had 30 women, but everything else was correct. Create a new 95% confidence interval based on this information.

(c) Your boss comes back and tells you that they made a mistake and the 0.5 inch standard deviation was actually just the sample standard deviation and we don’t know the true value. In addition, it turns out there were only 10 women in the study. After calming down, create a new 95% confidence interval based on this information.

Health researchers believe that the neonatal mortality rate is higher at home (MRH) than that in the health centers (MRC). The neonatal mortality rates (both MRH and MRC) for 20 countries are recorded in SSPS file Ass_2Q2.sav. can you solve it using equations

1. Do the data support researchers’ beliefs? Use α=0.05.
2. Find a 95% confidence interval to investigate the researchers’ belief and explain its meaning.
3. Check the assumptions of the above procedure.

A service station owner believes that an equal number of customers prefer to buy gasoline on every day of the week. A manager at the service station disagrees with the owner and claims that the number of customers who prefer to buy gasoline on each day of the week varies. Test the manager’s claim using alpha = 0.10. The owner surveyed 739 customers over a period of time to record each customer’s preferred day of the week. Here is what he found.

Draw a conclusion and interpret the decision.

Calculate the test statistic, x^(2), for a chi-squared test for association using the following table.
The following data represents the observed values and expected values of the eating habits of runners and swimmers for a random sample of adult athletes.