Suppose individual X scores in the population follow a normal distribution N(38, 20). A researcher draws numerous samples of sample size n = 100 from the population, and in each sample, she calculates the sample mean. Then 68% of these sample means should approximately fall within Group of answer choices (A) 34 and 40 (B) 34 and 38 (C) 38 and 44 (D) 36 and 40

In this hypothetical case study, a new rapid test kit nicknamed Alpha is being reviewed. The sensitivity of Alpha is 93.0% (0.93) and the specificity is 96.0% (0.96). Assume that the actual prevalence of the Zika antibody among the United States population of blood donors is 4% (0.04) and that of the hurricane disaster relief volunteers returning from Puerto Rico is 20.0% (0.20).

Construct a separate 2 x 2 table, to calculate the PPV and NPV for a population of 2,500 volunteers who aided in the recent hurricane relief efforts in the Caribbean.

If sensitivity and specificity remain constant, what is the relationship of prevalence to predictive-value positive and predictive-value negative? (Hint: Think if one increases, decreases, or stays the same.)

Let X~Bin(100,0.5).

Show all workings in details

a) Find the probability that X is a perfect square.

b) Find the probability that X is a greater than 60.

c) Find the expected value and variance of X.

1. A pharmacy is using X bar and R charts to record the time it takes to fill a prescription after the customer has turned in or called in the prescription. Each day, the pharmacy records the times it takes to fill six prescriptions. During a 30-day period, the hospital obtained the following values: X double bar = 20 minutes; R bar = 4 minutes. The upper and lower specifications are 23 minutes and 13 minutes respectively. What is the value of 6 sigma, to one decimal place?

Based on a recent​ study, the pH level of the arterial cord​ (one vessel in the umbilical​ cord) is normally distributed with mean 7.36 and standard deviation of 0.11. Find the percentage of preterm infants who have the following arterial cord pH levels.

a. pH levels between 7.00 and 7.50.

b. pH levels over 7.44.

A pharmaceutical company is testing a new drug to increase memorization ability. It takes a sample of individuals and splits them randomly into two groups. After the drug regimen is completed, all members of the study are given a test for memorization ability with higher scores representing a better ability to memorize. Those 23 participants on the drug had an average test score of 31.622 (SD = 4.794) while those 21 participants not on the drug had an average score of 32.04 (SD = 5.335). You use this information to create a 95% confidence interval for the difference in average test score. What is the margin of error? Assume the population standard deviations are equal.

2.     The dataset QuizPulse10 contains pulse rates collected from 10 students in a class lecture and then from the same ten students during a quiz. We might expect the mean pulse rate to increase under the stress of a quiz. Use the dataset to test at the 5% significance level whether there is evidence to support this claim.

a.     Perform the hypothesis test in Minitab.

b.    Make a decision and mathematically justify your decision

c.     Interpret the results.

Do out-of-state motorists violate the speed limit more frequently than in-state motorists? This vital question was addressed by the highway patrol in a large eastern state. A random sample of the speeds of 2,500 selected cars was categorized according to whether the car was registered in the state or in some other state and whether or not the car was violating the speed limit. The data follow.

In state speeding cars: 521

Out of state speeding cars: 328

In state not speeding cars: 1141

Out of state not speeding cars: 510

a.) Do these data provide enough evidence to support the highway patrol's claim at the 5% significance level? Your conclusion must be in terms of the P-Value. Show all necessary work.

b). What type of error is possible and describe this error in terms of the problem?

c). Estimate the difference in the actual percentage of In State and Out of State speed limit violators using a 95% confidence interval. Show all necessary work. Using this interval estimation, is there sufficient evidence to support the highway patrol's claim? Explain Carefully.

d). Carefully interpret the confidence interval estimation.

1. A researcher who works for a national retail chain is interested in changes in employee satisfaction during the holiday season. The table below contains employee satisfaction scores taken at two time points (August 1^st and December 1^st) from a sample of 12 employees. Higher scores indicate more satisfaction. Conduct a hypothesis test to determine if there is an increase or decrease in employee satisfaction from Time 1 to Time 2. Use alpha .05.

1. State the null alternative hypothesis.
2. Conduct the hypothesis test.
3. State your findings.
4. Report an effect size measure. Please use the formula that we used in class

For a data set obtained from a sample of size n = 121 with x- = 44.25, it is known that σ = 5.4.

(a) What is the point estimate of µ?

(b) Find z score corresponding to a 95% confidence level, z_α/2. Recall that (1 − α)100% = 95%.

(c) Construct a 95% confidence interval for µ.

(d) What is the margin of error in part (c)?

3. The outside diameter of a part used in a gear assembly is known to be normally distributed with a mean of 39 mm and a standard deviation of 2.5 mm. The specifications on the diameter are (36,45), which means that part diameters between 36 mm and 45 mm are considered acceptable.

1. What is the proportion nonconforming?
2. What is Z bench?
3. If the mean of the process was centered between the specs, what would the proportion non-conforming be?

Chi-square tests are nonparametric tests that examine nominal categories as opposed to numerical values. Consider a situation in which you may want to transform numerical scores into categories. Provide a specific example of a situation in which categories are more informative than the actual values.

Suppose we had conducted an ANOVA, with individuals grouped by political affiliation (Republican, Democrat, and Other), and we were interested in how satisfied they were with the current administration. Satisfaction was measured on a scale of 1-10, so it was measured on a continuous scale. Explain what changes would be required so that you could analyze the hypothesis using a chi-square test. For instance, rather than looking at test scores as a range from 0 to 100, you could change the variable to low, medium, or high. What advantages and disadvantages do you see in using this approach? Which is the better option for this hypothesis, the parametric approach or nonparametric approach? Why?"

Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 17.5 customer contacts per week. The sample standard deviation was 5.4. Provide 90% and 95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel.

90% confidence interval, to 2 decimals:

( ,  )

95% confidence interval, to 2 decimals:

( , )

Three randomly selected households are surveyed as a pilot project for a larger survey to be conducted later. The numbers of people in the households are 2, 4, and 10. Consider the values of 2, 4, and 10 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 4, and 10. The nine different samples are as follows: (2, 2), (2, 4), (2, 10), (4, 2), (4, 4), (4, 10), (10, 2), (10, 4), and (10, 10). (i) Find the mean of each of the nine samples, then summarize the sampling distribution of the means in the format of a table representing the probability distribution. (ii) Compare the population mean to the mean of the sample means. (iii) Do the sample means target the value of the population mean? In general, do means make good estimators of population means? Why or why not?