A medical researcher wants to begin a clinical trial that involves systolic blood pressure (SBP) and cadmium (Cd) levels. However, before starting the study, the researcher wants to confirm that higher SPB is associated with lower Cd levels. Below are the SBP and Cd measurements for a sample a participants. What can the researcher conclude with an α of 0.10?

a) What is the appropriate statistic?
---Select--- na Correlation Slope Chi-Square
Compute the statistic selected in a):

b) Obtain/compute the appropriate values to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

There was a significant positive relationship between systolic blood pressure and cadmium levels.There was a significant negative relationship between systolic blood pressure and cadmium levels.    There was no significant relationship between systolic blood pressure and cadmium levels.

CNNBC recently reported that the mean annual cost of auto insurance is 975 dollars. Assume the standard deviation is 262 dollars, and the cost is normally distributed. You take a simple random sample of 37 auto insurance policies. Round your answers to 4 decimal places.

What is the distribution of XX? XX ~ N(,)

What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)

What is the probability that one randomly selected auto insurance is more than $937?

a simple random sample of 37 auto insurance policies, find the probability that the average cost is more than $937.

For part d), is the assumption of normal necessary? YesNo

The following table summarizes the weights in kg of 40 students in this class:

Determine a 10% random sample of the heights using the following three methods, and explain how you selected them.  You may use a deck of cards, a random number table, RAND() in Excel or some other method to generate random numbers.

a. Random sampling

b. Systematic Random Sampling

c. Stratified Random Sampling

d. What is the sampling error for each method?

1. Consider the process {X_t} in which X_t = Z_t + 0.5Z_t-1 - 2Z_t-2. Investigate the
stationarity of the process under the following conditions. Calculate the ACF for the
stationary models.
(a) Zt ~ WN(0,(sigma)²) ; (sigma)² < infinity
(b) {Z_t } is a sequence of i.i.d random variables with the following distribution:
fz_t(z) = 2/z³ ; z > 1

Week 2: Probabilities in Real World

Look online and find an article published within the past 4 weeks that includes a reference to probabilities, means, or standard deviations. These articles might be discussing weather events, investing outcomes, or sports performance, among many other possible topics.

Your first post should include a summary of the article and what numbers you are highlighting from that article. Also include a link to the actual article.

Suppose x is a random variable with a mean of 40 and a standard deviation of 6.5 that is not necessarily normally distributed.

(a) If random samples of size n=20 are selected, can you say the sampling distribution of the means, the (x bar) distribution, is normally distributed? why or why not?

(b) if random samples of size n=64 are selected, what can you say about the sampling distribution of the means, (x bar)? is it normally distributed? what is μ _(x bar) ? what is the standard error?

6. Your statistics professor is involved in another educational outreach program designed to decrease participants’ levels of stress. She designed a study in which participants were randomly assigned to two groups. One group completed a 30-minute meditation. A second, control group watched television for 30-minutes. After 30 minutes, participants reported their level of stress.

Your professor, again, asks for your assistance. She predicts that the average level of stress will differ significantly between the meditation and control groups. She wants to use an alpha level of 0.05. (50 Points)

a. Are you running a one-tailed or two-tailed test?

b. Write your alternative and null hypotheses.

c. Which statistical analysis will you use to run your test (e.g. one-sampled t-test, an independent-samples t-test, a paired t-test, or chi-square test)?

d. Run your statistical analysis using SPSS.

(Remember, if you are running a one-tailed test, your alpha value is located in one-tail, meaning your p-value needs to be less than 0.05 to reject the null hypothesis.

If you are running a two-tailed test, your alpha value is divided in half, meaning your p-value needs to be less than 0.025 to reject the null hypothesis)

A pharmaceutical company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of mercury) for nine patients before taking the new drug and 22 hours after taking the drug are shown in the table below. Is there enough evidence to support the company's claim?

Let d=(blood pressure before taking new drug)−(blood pressure after taking new drug)d=(blood pressure before taking new drug)−(blood pressure after taking new drug). Use a significance level of α=0.01 for the test. Assume that the systolic blood pressure levels are normally distributed for the population of patients both before and after taking the new drug.

Step 1 of 5: State the null and alternative hypotheses for the test.

Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5: Make the decision for the hypothesis test. Reject or Fail to Reject.

Michael and Greg share an apartment 10 miles from campus. Michael thinks that the fastest way to get to campus is to drive the shortest route, which involves taking several side streets. Greg thinks the fastest way is to take the route with the highest speed limits, which involves taking the highway most of the way but is two miles longer than Michael’s route. You recruit 50 college friends who are willing to take either route and time themselves. After compiling all the results, you found that the travel time for Michael’s route follows a Normal distribution with mean equal to 30 minutes and standard deviation equal to 5 minutes. Greg’s route follows a Normal distribution with a mean equal to 26 minutes and a standard deviation of 9.5 minutes.

1)Which route is faster and why?

2)Which route is more reliable and why?

3) Suppose that you leaving home headed for a University exam. Obviously, you don’t want to be late. You are leaving home at 5:15 and the exam is at 6:00PM. Which route would you take to avoid being late and why? Show your calculations.

A program for generating random numbers on a computer is to be tested. The program is instructed to generate 100 single-digit integers between 0 and 9. The frequencies of the observed integers were as follows. At the 0.05 level of significance, is there sufficient reason to believe that the integers are not being generated uniformly?

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


(ii) Find the p-value. (Round your answer to four decimal places.)


(b) State the appropriate conclusion.

Reject the null hypothesis. There is not significant evidence that the integers are not being generated uniformly. Fail to reject the null hypothesis. There is significant evidence that the integers are not being generated uniformly.     Reject the null hypothesis. There is significant evidence that the integers are not being generated uniformly. Fail to reject the null hypothesis. There is not significant evidence that the integers are not being generated uniformly.

A grading scale is set up for 1000 students’ test scores. It is assumed that the scores are normally distributed with a mean score of 80 and a standard deviation of 10:

a)    What proportion of students will have scores between 40 and 85?

b)    If 60 is the lowest passing score, what proportion of students pass the test?

c)    What score would a student have to score to be in the 68^th percentile?

d)    What score would a student have to make to be in the top 20% of the class?

e) If 60 is the lowest passing score, estimate how many students pass the test?

Suppose that a continuous, positive random variable T has a hazard function defined by

h(t) = h_j when a_j-1 ≤ t < a_j,   j = 1, 2, …, k,

where a₀ = 0 and a_k= ∞, a₀ < a₁ < … < a_k   and   h_j> 0, j = 1, 2, …, k.

(a) Express S(t), the survivor function of T, in terms of the h_j’s.

(b) Express f(t), the probability density function of T, in terms of the h_j’s.

(c) If you observe a random sample of size n of the form (t₁, δ₁), …, (t_n, δ_n), where δ_i = 1 if t_i is a failure time, and 0 if t_i is a right-censoring time, derive the maximum likelihood estimates of the h_j’s and, hence, the maximum likelihood estimate of S(t).

(d) What happens to the maximum likelihood estimate of S(t) as k becomes “large” and the distances a_j– a_j-1get “small”?

The melting point (in degrees Fahrenheit) for a randomly selected tub of margarine of a certain brand is known to have a normal distribution with a SD, σ = 1.21. A sample of n = 5 tubs of margarine is drawn. The sample mean of melting temperature is computed to be ¯x = 95.3. (a) Construct a 95% confidence interval for the mean melting temperature. (b) Construct a 99% confidence interval for the mean melting temperature. Compare the width of the two intervals in (a) and (b)? (c) Did you use the central limit theorem to construct the intervals in (a) and (b)? Explain.

7.40 People were asked whether they agreed or disagreed with the statement that there is only one true love for each person. The table below gives a two-way table showing the answers to this question as well as the education level of the respondents. A person’s education is categorized as HS (high school degree or less), Some (some college) or College (college graduate or higher). Is the level of a person’s education related to how the person feels about one true love? If there is a significant association between these two variables, describe how they are related.

The mean of a normal probability distribution is 410; the standard deviation is 105. a. μ ± 1σ of the observations lie between what two values? Lower Value Upper Value b. μ ± 2σ of the observations lie between what two values? Lower Value Upper Value c. μ ± 3σ of the observations lie between what two values? Lower Value Upper Value