For the following questions, use the research question and context to determine the type of test required:

1. A researcher is interested in knowing whether the proportion of people who live past the age of 80 differs. She takes a sample from the local records of 100 people who had lived in each region for at least 40 years. In region X, 44% live past 80 years of age. In region Y, only 38% live past the age of 80. Is this evidence of a significant difference? * \

a.one-sample z-test

b.one-sample t-test

c.two-sample z-test

d.two-sample t-test

2. In a particular community it is know that about 8% of residents age 18-25 use recreational marijuana. A social services provider has run a targeted campaign to try to reduce the use of marijuana in favor of healthy endorphin-enhancing activities such as exercise. After the campaign, her team gathers data from a sample of 150 residents age 18-25 in the region, 7% of whom say they use marijuana for recreation. Is this evidence that the proportion has decreased? *

a.one-sample z-test

b.one-sample t-test

c.two-sample z-test

d.two-sample t-test

3. A researcher would like to investigate whether a particular drug shows adverse effects more often for those aged 45 and above versus those who are younger. They examine a sample of 400 patients who have taken the drug and been monitored by a pharmaceutical agency. For each patient they record the patient's age and examine whether the patient reported any side effects. *

a.one-sample z-test

b.one-sample t-test

c.two-sample z-test

d.two-sample t-test

4. A researcher would like to investigate whether a particular drug shows higher levels of adverse effects for those aged 45 and above versus those who are younger. They examine a sample of 400 patients who have taken the drug and been monitored by a pharmaceutical agency. For each patient they record the patient's age and examine the rating (on a scale 0-10) the patient reported for a possible side effect.

a.one-sample z-test

b.one-sample t-test

c.two-sample z-test

d.two-sample t-test

5. In a study conducted in order to investigate the relationship between blood pressure reduction and consumption of fish oil (Knapp & Fitzgerald, 1989; from Phannkuch et al. 2015), researchers randomly assigned 14 male volunteers with high blood pressure to one of two diets: a fish oil diet and a regular oil diet. Each participant’s blood pressure was measured at the beginning and end of the study, and the reduction (Pre – Post), in millimeters of mercury, was recorded. On average, the Fish oil group’s blood pressure reduction was 7.71 mm better than the Regular oil group. *

a.one-sample z-test

b.one-sample t-test

c.two-sample z-test

d.two-sample t-test

6. There is increasing concern about misuse of antimicrobial drugs (such as antibiotics) that are designed to kill microorganisms and stop their growth. Bacterial resistance is on the rise, and it has been found in previous studies that 30-50% of inpatient antimicrobial use is inappropriate. This raises questions about what characteristics of medical facilities are indicative of lower antibiotic use. ....In a study by Chau et al. (2016), published in a journal called Infection control and hospital epidemiology, it was found that facilities that had at least one full-time attending infectious disease specialist had significantly lower average antibiotics use. *

a.one-sample z-test

b.one-sample t-test

c.two-sample z-test

d.two-sample t-test

Consider a flight of stairs with ? stairs. Larry Bird can take one, two or three stairs in a single stride. Find a recurrence relation for ?(?), the number of different ways that Larry Bird can traverse the stairs. Give both the initial conditions (?(1), ?(2) and ?(3)), as well as the recurrence relation for ?(?), with ? ≥ 3.

5.

How can the 24 month distribution of HIV stigma scores for the intervention groups be described in terms of shape?

For this problem, five cotton varieties were selected from a larger study of yield stability. The objective was to determine if there are differences among the mean weight of the fiber for these varieties and if so, in the next homework problem to determine those differences. For each variety, data were collected at harvest from four plots of each variety in the yield stability test. The researcher recorded the data in units of “thousands of fibers per seed.” There were no missing data.

1. (a) Identify the populations and random variables of interest.

2. (b) Give a model for this study (i.e, the distributions of the random variables and all other statistical

   assumptions).

3. (c) Set up an appropriate initial set of hypothesis to be tested. Give the test statistic and its

   distribution. Using " = 0.01, give the critical region for the test.

4. (d) SAS® was used to carry out an analysis of variance. From the computer output,

   SSVarieties = 57.0636 and SSError = 23.0537.

   Use this information to test your initial hypothesis using the test that you set up in part (c). Summarize your calculations in analysis of variance (ANOVA) table. Your conclusion must be stated in the context of the problem.

The supervisor of a manufacturing plant is trying to determine how many of two parts, Part X and Part Y, are to be produced per day. Each part must be processed in three sections of the plant. The time required for the production along with the profit contribution for each part are given in the following table. Time required (Minutes/Unit) Section 1 Section 2 Section 3 Profit/Unit Part X 50 30 18 $2 Part Y 80 45 22 $3 Available time (minutes) 3,600 2,500 1,200 ​ No more than 60 units of Part X and up to 70 units of Part Y can be produced per day.

​a.What are the variables and the objective function?

b. Develop a linear programming model and solve the model to determine the optimal production quantities of Parts X and Y and solve with graphing. No need to include the graph , but please include the corner points for the feasible region

c. What is the maximum profit

In a random sample of 39 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 66

​months, with a standard deviation of 14 months. Construct and interpret a 95​%confidence interval for the mean length of sentencing for this crime.

The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 900 voters in the town and found that 66% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is over 62%. Testing at the 0.02 level, is there enough evidence to support the strategist's claim?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places. The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 900 voters in the town and found that 66% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is over 62%. Testing at the 0.02 level, is there enough evidence to support the strategist's claim?

Step 3 of 6: Specify if the test is one-tailed or two-tailed. The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 900 voters in the town and found that 66% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is over 62%. Testing at the 0.02 level, is there enough evidence to support the strategist's claim?

Step 4 of 6: Determine the decision rule for rejecting the null hypothesis, H0. The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 900 voters in the town and found that 66% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is over 62%. Testing at the 0.02 level, is there enough evidence to support the strategist's claim?

Step 5 of 6: Make the decision to reject or fail to reject the null hypothesis. The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 900 voters in the town and found that 66% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is over 62%. Testing at the 0.02 level, is there enough evidence to support the strategist's claim?

Step 6 of 6: State the conclusion of the hypothesis test.

Customers are arriving to a shop according to Poisson process with mean 3.2 customers/hour. What is the probability that the next customer will arrive after 10 minutes but before 33 minutes?

A study was made on the amount of converted sugar in a certain process at various temperatures. The data were coded and recorded as follows:

1. Estimate the linear regression line.
2. Estimate the mean amount of converted sugar produced when coded temperature is 1.75.
3. Estimate the conditional standard deviation of converted sugar on temperature.
4. Estimate the correlation coefficient of converted sugar on temperature.
5. Determine and plot data, the regression line and the 90% confidence interval of the above regression equation in the same plot.

A United Nations report shows the mean family income for Mexican migrants to the United States is $28,120 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 27 Mexican family units reveals a mean to be $39,750 with a sample standard deviation of $12,765. Does this information disagree with the United Nations report? Apply the 0.01 significance level.

In a study of cell phone use and brain hemispheric dominance, an internet survey was emailed to 2601 subjects randomly selected from an online group involved with ears. 975 surveys were returned. Construct a 90% confidence interval for the proportion of returned surveys. a) What is the best point estimate of the population P c) Construct the confidence level b) Identify the value of the margin of error E. c) Construct the confidence level.

Assume a normal distribution for each question.

(a) What proportion of the distribution consists of z-scores greater than 0.25? (

b) What is the probability of obtaining a z-score less than 0.50? (

c) What is the probability of obtaining a z-score greater than −1.50?

(d) What is the probability of obtaining a z-score between +1.00 and −1.00?

A small dairy wants to make sure that their butter mill is producing bricks of butter that do not differ from the labelled weight by too much. The machine produces 30 bricks of butter per minute and runs for 4 hours Monday, Tuesday, and Wednesday mornings. If the weights of the bricks of butter are deemed to be too high or too low then that afternoon will be dedicated to recalibrating the machines.

Question 1.

Use a hypothesis test to determine if Monday's sample indicates we should recalibrate the butter mill.

• a. What are my hypotheses? State them in both words and as equations.
• b. Every hundredth brick is weighed and the weight difference recorded.
  • Suppose we know the sample values are normally distributed.
  • On Monday the sample yielded an average of weight differences of -2.5 g and a sample standard deviation of 10.25 g.
  • Let ?X be a random variable representing the difference between the actual weight of a brick of butter and the desired weight of the brick of butter.
  • Write the short hand for the distribution of ?¯X¯ (the sampling distribution for the sample means).
• c. Draw the sampling distribution.
• d. Complete the hypothesis test using ?=0.03α=0.03.
  • Shade the region for the p-value
  • Compute the p-value.
  • Compare the p-value to the critical value.
• e. Write the conclusion in terms of what the dairy owner should plan to do Monday afternoon.

Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.4 and a mean diameter of 212 inches.

If 80 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.1 inches? Round your answer to four decimal places.