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.
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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.
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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?
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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.
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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?
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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?
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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.
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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.
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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
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The population proportion is 0.28. What is the probability that a sample proportion will be within ±0.04 of the population proportion for each of the following sample sizes? (Round your answers to 4 decimal places.)
(a)n = 100
(b)n = 200
(c)n = 500
(d)n = 1,000
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(R programming)
Generate 50 samples from a Poisson distribution with lambda to be 2 and define the log likelihood function
Use optimization to find the maximum likelihood estimator of lambda. Repeat for 100 times using forloop. You will need to save the results of the estimated values of lambda.
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| As the climate grows warmer, we expect many animal species to move towards the poles in an attempt to maintain their |
| preferred temperature range. Do data on fish in the North Sea confirm this expectation? Data for 25 years, 1977 through 2001, |
| on mean winter temperatures at the bottom of the North Sea (degrees Celsius) and on the center of the distribution of anglerfish |
| in degrees of North latitude are given below. Does the fish distribution depend on temperature? |
| Year | Degrees North Latitude | Temp (oC) |
| 1977 | 57.20 | 6.26 |
| 1978 | 57.96 | 6.26 |
| 1979 | 57.65 | 6.27 |
| 1980 | 57.59 | 6.31 |
| 1981 | 58.01 | 6.34 |
| 1982 | 59.06 | 6.32 |
| 1983 | 56.85 | 6.37 |
| 1984 | 56.87 | 6.39 |
| 1985 | 57.43 | 6.42 |
| 1986 | 57.72 | 6.52 |
| 1987 | 57.83 | 6.68 |
| 1988 | 57.87 | 6.76 |
| 1989 | 57.48 | 6.78 |
| 1990 | 58.13 | 6.89 |
| 1991 | 58.52 | 6.9 |
| 1992 | 58.48 | 6.93 |
| 1993 | 57.89 | 6.98 |
| 1994 | 58.71 | 7.02 |
| 1995 | 58.07 | 7.09 |
| 1996 | 58.49 | 7.13 |
| 1997 | 58.28 | 7.15 |
| 1998 | 58.49 | 7.29 |
| 1999 | 58.01 | 7.34 |
| 2000 | 58.57 | 7.57 |
| 2001 | 58.90 | 7.65 |
a)
| Ho: | |
| Ha: | |
| test-statistic: | |
| df: | |
| Exact P value for the test-statistic | |
| Conclusion relative to the hypothesis: | |
| ts= ,df= ,P= |
b)
| What is the equation for the regression? |
c)
|
What is the estimate of the amount of variance in Y which is due to its regression on the independent variable? |
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In international Morse code, each letter in the alphabet is symbolized by a series of dots and dashes: the letter “a” for example is encoded as “×- ” while the most common letter “e” has the shortest code “×” (just a dot). What is the minimum number of dots and/or dashes needed to represent any letter in the English alphabet (26 letters)?
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1. What is the mean of the sample values 2 cm, 2 cm, 3 cm, 5 cm, and 8 cm?
2. What is the median of the sample values listed in Exercise 1?
3. What is the mode of the sample values listed in Exercise 1?
4. If the standard deviation of a data set is 5.0 ft, what is the variance?
5. If a data set has a mean of 10.0 seconds and a standard deviation of 2.0 seconds, what is the z score corresponding to the time of 4.0 seconds?
6. Fill in the blank: The range, standard deviation, and variance are all measures of _____.
7. What is the symbol used to denote the standard deviation of a sample, and what is the symbol used to denote the standard deviation of a population?
8. What is the symbol used to denote the mean of a sample, and what is the symbol used to denote the mean of a population?
9. Fill in the blank: Approximately _____ percent of the values in a sample are greater than or equal to the 25th percentile.
10. True or false: For any data set, the median is always equal
to the 50th percentile.
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A consumer is trying to decide between two long-distance calling plans. The first one charges a flat rate of 10 cents per minute. The second charges a flat rate of 99 cents for calls up to 20 minutes in duration and then 10 cents for each additional minute exceeding 20. (Assume that calls lasting a non-integer number of minutes are charged proportionately to a whole-minutes charge). If the duration of a randomly selected call of this consumer is exponentially distributed and its expected value is 15 minutes, compute the expected value of the corresponding charge by each plan.
Hint: Denote by X the duration of a random call, by Y1 the charge of the first plan, and by Y2 the charge of the second plan. Then, express Y1 and Y2 as functions of X, i.e., Y1 = h1(X) and Y2 = h2(X)
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