In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists wants to test a new medication to see if it has either a positive or negative effect on intelligence, or no effect at all. A sample of 30 participants who have taken the medication has a mean of 105. It is assumed that the data are drawn from a normally distributed population. Did the medication affect intelligence, using α = 0.05?

(a) State hypotheses appropriate to the research question.

(b) Describe what test would you use and state the reasons for your choice.

(c) Draw a conclusion in the context of the problem using the p-value.

(d) Construct a 95% CI for µ. Conclude in the context of the problem.

(e) Compute the power if the true population mean is 110.

home / study / math / statistics and probability / statistics and probability questions and answers / suppose that we fit model (1) to the n observations (y1, x11, x21), …, (yn, x1n, x2n). yi ... Your question has been answered Let us know if you got a helpful answer. Rate this answer Question: Suppose that we fit Model (1) to the n observations (y1, x11, x21), …, (yn, x1n, x2n). yi = β0 + ... Suppose that we fit Model (1) to the n observations (y1, x11, x21), …, (yn, x1n, x2n). yi = β0 + β1x1i + β2x2i + εi , i = 1, …., n, (1) where ε’s are identically and independently distributed as a normal random variable with mean zero and variance σ2, i = 1, …, n , and all the x’s are fixed. a) Suppose that Model (1) is the true model. Show that at any observation yi , the point estimator of the mean response and its residual are two statistically independent normal random variables. b) Suppose the true model is Model (1), but we fit the data to the following Model (2) (that is, ignore the variable x2). yi = β 0 + β 1x1i + εi , i = 1, …., n. Assume that average of x1 =0, average of x2=0. The sum of x1i and x2i equals 0. Derive the least-squares estimator of β1 obtained from fitting Model (2). Is this least-squares estimator biased for β1 under Model (1)?

Quality Associates, Inc., a consulting firm, advises its clients about sampling and statistical procedures that can be used to control their manufacturing processes. In one particular application, a client gave Quality Associates a sample of 800 observations taken while that client’s process was operating satisfactorily. The sample standard deviation for these data was 0.21; hence, with so much data, the population standard deviation was assumed to be 0.21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis. By analyzing the new samples, the client could quickly learn whether the process was operating satisfactorily. When the process was not operating satisfactorily, corrective action could be taken to eliminate the problem. The design specification indicated that the mean for the process should be 12. The hypothesis test suggested by Quality Associates is as follows: ± H H :1 2 :1 2 0 a m m 5 Corrective action will be taken any time H0 is rejected. The samples listed in the following table were collected at hourly intervals during the first day of operation of the new statistical process control procedure. These data are available in the file Quality. Sample 1 Sample 2 Sample 3 Sample 4 11.55 11.62 11.91 12.02 11.62 11.69 11.36 12.02 11.52 11.59 11.75 12.05 11.75 11.82 11.95 12.18 11.90 11.97 12.14 12.11 11.64 11.71 11.72 12.07 11.64 11.71 11.72 12.07 11.80 11.87 11.61 12.05 12.03 12.10 11.85 11.64 11.94 12.01 12.16 12.39 11.92 11.99 11.91 11.65 12.13 12.20 12.12 12.11 12.09 12.16 11.61 11.90 11.93 12.00 12.21 12.22 12.21 12.28 11.56 11.88 12.32 12.39 11.95 12.03 11.93 12.00 12.01 12.35 11.85 11.92 12.06 12.09 11.76 11.83 11.76 11.77 12.16 12.23 11.82 12.20 11.77 11.84 12.12 11.79 12.00 12.07 11.60 12.30 12.04 12.11 11.95 12.27 11.98 12.05 11.96 12.29 12.30 12.37 12.22 12.47 12.18 12.25 11.75 12.03 11.97 12.04 11.96 12.17 12.17 12.24 11.95 11.94 11.85 11.92 11.89 11.97 12.30 12.37 11.88 12.23 12.15 12.22 11.93 12.25 1. Conduct a hypothesis test for each sample at the 0.01 level of significance and determine what action, if any, should be taken. Provide the test statistic and p value for each test. 2. Compute the standard deviation for each of the four samples. Does the conjecture of 0.21 for the population standard deviation appear reasonable? 3. Compute limits for the sample mean x around 12 m 5 such that, as long as a new sample mean is within those limits, the process will be considered to be operating satisfactorily. If x exceeds the upper limit or if x is below the lower limit, corrective action will be taken. These limits are referred to as upper and lower control limits for quality-control purposes. 4. Discuss the implications of changing the level of significance to a larger value. What mistake or error could increase if the level of significance is increased? Can you show it in excel of how you get the answers, Thanks

What is the purpose of using correlation as well as the interpretation of the correlation coefficient? In your video response, please describe at least 2 examples of an extremely low relationship among variables and an extremely high relationship among variables. Finally, discuss the two most common statistical techniques for determining relationships of variables.

A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a​ two-candidate election, if a specific candidate receives at least 55​% of the vote in the​ sample, that candidate will be forecast as the winner of the election. You select a random sample of 100 voters. Complete parts​ (a) through​ (c) below.

a. What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 50.1​%? The probability is nothing that a candidate will be forecast as the winner when the population percentage of her vote is 50.1​%. ​(Round to four decimal places as​ needed.)

b.

c.

d.

In a random sample of 13 residents of the state of Washington, the mean waste recycled per person per day was 1.6 pounds with a standard deviation of 0.43 pounds. Determine the 98% confidence interval for the mean waste recycled per person per day for the population of Washington.

Statistical significance tests do not tell the researcher what we want to know nor do they evaluate whether or not our results are important. They tell us only whether or not the results of a study were due to chance. Therefore, how do researchers go about doing this? In your video response, please discuss the relationship of the p-value in relation to the level of significance. Lastly, please provide an example of a Type I and Type II errors.  

Pinworm: In Sludge County, a sample of 40 randomly selected citizens were tested for pinworm. Of these, 8 tested positive. The CDC reports that the U.S. average pinworm infection rate is 12%. Test the claim that Sludge County has a pinworm infection rate that is greater than the national average. Use a 0.10 significance level.

(a) What is the sample proportion of Sludge County residents with pinworm? Round your answer to 3 decimal places. p̂ =

(b) What is the test statistic? Round your answer to 2 decimal places. zp hat =

(c) What is the P-value of the test statistic? Round your answer to 4 decimal places. P-value =

(d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0

(e) Choose the appropriate concluding statement.

The data supports the claim that the infestation rate in Sludge County is greater than the national average.

There is not enough data to support the claim that that the infestation rate in Sludge County is greater than the national average.

We reject the claim that the infestation rate in Sludge County is greater than the national average.

We have proven that the infestation rate in Sludge County is greater than the national average.

A teacher gives the following assignment to 200 students: Check the local newspaper every morning for a week and count how many times the word “gun” is mentioned on the “local news” pages. At the end of the week, the students report their totals. The mean result is 85, with a standard deviation of 8. The distribution of scores is normal. a. How many students would be expected to count fewer than 70 cases? b. How many students would be expected to count between 80 and 90 cases? c. Karen is a notoriously lazy student. She reports a total of 110 cases at the end of the week. The professor tells her that he is convinced she has not done the assignment, but has simply made up the number. Are his suspicions justified?

The multiple regressions serve to explain the behavior of one variable (dependent variable) though a set of some explanatory variables for which we can find a logical/theoretically founded relationship with the dependent variable.

Please discuss three business situations (either real or a business situation) with proposed set of 5 explanatory variable. Could you define the expected sign (positive or negative) of these selected explanatory variables?

As e have discussed the usage of the dummy variables propose at least in one of the three cases you discuss previously one or two dummy variables you think are good explanatory variables for the case you are discussing.

Another researcher is interested in how caffeine will affect the speed with which people read but decides to include a third condition, a placebo group (a group that gets a pill that looks like the caffeine group does, but it does not contain caffeine). The researcher randomly assigns 12 people into one of three groups: 50mg Caffeine (n1=4), No Caffeine (n2=4), and Placebo (n3=4). An hour after the treatment, the 12 participants in the study are asked to read from a book for 1 minute; the researcher counts the number of words each participant finished reading. The following are the data for each group:

50mg Caffeine (group 1)

450 400 500 450

No Caffeine (group 2)

400 410 430 440

Placebo (group 3)

400 410 430 440

Answer the following questions using the Analysis of Variance instead of the t-test

a. What is the research hypothesis?

b. What is the null hypothesis?

c. What is dfbetween and dfwithin? What is the total df for this problem?

d. What is SSbetween and SSwithin? What is the total SS for this problem?

e. What is MSbetween and MSwithin?

f. Calculate F.

Use an a-level of .05 to answer the questions below

g. Draw a picture of the F distribution for dfbetween and dfwithin above, and locate F on the x-axis.

h. What is the critical value of F, given dfbetween and dfwithin? Indicate the critical value of F (and its value) in your drawing. Also indicate what the area is in the tail beyond the critical value of F.

i. Can you reject the null hypothesis?

j. Can you accept the research hypothesis?

4. Two randomized-controlled trials of routine ultrasonography screening during pregnancy were carried out, to see whether routine ultrasound imaging influenced outcomes of pregnancy such as birthweight and mode of delivery. No significant differences were found. At ages 8 to 9 years, 2011 singleton children of the women who had taken part in these trials were followed up. Ultrasonography had actually been carried out on 92% of the ‘screened’ group and 5% of the control group. No significant differences were found in scores for reading, spelling, arithmetic or overall school performance. A subgroup of children underwent specific tests for dyslexia. The test results classified as dyslexic 21 of the 309 children in the screened group (7%, 95% confidence interval = 3-10%) and 26 of the 294 controls (9%, 95% CI = 4-12%]). (Lancet 1991; 339: 85-89.) a. What is meant by “randomized” and “controlled”? Why were these techniques used?

In a Randomized Complete Block Design one of the two factors in the analysis is an extraneous variable (we are not directly interested in it) that is called a block. Explain the goal of including the extraneous variable in the analysis.

Another paper, by Kristin Butcher and Anne Piehl (1998), compared the rates of institutionalization (in jail, prison, or mental hospitals) among immigrants and natives. In 1990, 7.54% of the institutionalized population (or 20,933 in the sample) were immigrants. The standard error of the fraction of institutionalized immigrants is 0.18. What is a 95% confidence interval for the fraction of the entire population who are immigrants? If you know that 10.63% of the general population at the time are immigrants, what conclusions can be made? Explain.

The mean of a population is 75 and the standard deviation is 12. The shape of the population is unknown. Determine the probability of each of the following occurring from this population. a. A random sample of size 35 yielding a sample mean of 78 or more b. A random sample of size 150 yielding a sample mean of between 73 and 76 c. A random sample of size 219 yielding a sample mean of less than 75.8