EEMB 146 Lecture Notes - Lecture 5: Sampling Distribution, Standard Error, Statistical Parameter

36 views3 pages

mauvechinchilla505

12 Apr 2018

School

UCSB

Department

Ecology, Evolution & Marine Biology

Course

EEMB 146

Professor

Briggs

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

Sampling distribution the probability distribution of values for an estimate that we might obtain when we sample a population. Taking a sample of n=5 from the distribution, and calculating the mean. The standard deviation of its sampling distribution an estimate of how far the sample mean is likely to be from the population mean. Different from standard deviation (s) a quantity calculated to indicate the extent of deviation for a group as a whole the degree to which individuals within the sample differ from the sample mean. But we rarely know the population standard deviation. So we can use the estimate sample standard deviation (s) and divide it by the square-root of population size (n) Bigger sample= smaller standard error for the mean. Confidence interval the range of values surrounding the sample estimate that is likely to contain the population parameter. We can say: we are 95% confident that the true mean lies between 5. 9 and 13. 7 .

Related Questions

(15.28) Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score Î¼Î¼ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 6.4. Suppose that (unknown to you) the mean score of those taking the MCAT on your campus is 24.

In answering the following, use z-scores rounded to two decimal places.

If you choose one student at random, what is the probability (Â±Â±0.0001) that the student's score is between 20 and 30?

You sample 22 students. What is the standard deviation (Â±Â±0.01) of the sampling distribution of their average score xÂ¯Â¯Â¯xÂ¯?

What is the probability (Â±Â±0.0001) that the mean score of your sample is between 20 and 30?

maroonhyena890

1. You are given only three quarterly seasonal indices and quarterly seasonally adjusted data for the entire year. What is the raw data value for Q4? Raw data is not adjusted for seasonality.

Quarter Seasonal Index Seasonally Adjusted Data

Q1 .80 295

Q2 .85 299

Q3 1.15 270

Q4 --- 271

2. One model of exponential smoothing will provide almost the same forecast as a liner trend method. What are linear trend intercept and slope counterparts for exponential smoothing?

A. Alpha and Delta

B. Delta and Gamma

C. Alpha and Gamma

D. Standard Deviation and Mean

3. When performing correlation analysis what is the null hypothesis? What measure in Minitab is used to test it and to be 95% confident in the significance of correlation coefficient.

A. Ho: r = .05 p < .5

B. Ho: r = 0 p >.05

C. Ho: r ? 0 p?.05

D. Ho: r = 0 p?.05

In decomposition what does the cycle factor (CF) of .80 represent for a monthly forecast estimate of a Y variable?

A. The estimated value is 80% of the average monthly seasonal estimate.
B. The estimate is .80 of the forecasted Y trend value.
C. The estimated value is .80 of the historical average CMA values.
D. The estimated value has 20% more variation than the average historical Y data values.

5. A Wendy's franchise owner notes that the sales per store has fallen below the stated national Wendy's outlet average of $1,368,000. He asserts a change has occurred that reduced the fast food eating habits of Americans. What is his hypothesis (H1) and what type of test for significance must be applied?

A. H1: u ? $1,368,000 A one-tailed t-test to the left.
B. H1: u = $1,368,000 A two-tailed t-test.
C. H1: u < $1,368,000 A one-tailed t-test to the left.
D. H1: p < $1,368,000 A one-tailed test to the right

6. As the sample size from a population increases, for a given level of significance what happens to the null hypothesis rejection region and size of the t-table value?

A. The rejection region and the t-table value generally gets smaller for sample size below 31.
B. The rejection region gets larger and the t-table value generally gets smaller for sample sizes below 31.
C. The rejection region remains unchanged while the t-table value gets smaller for all sample sizes.
D. The zero mean hypothesis region gets larger and the t-table value gets larger as well for sample sizes below 31.

7. You obtained autocorrelation LBQ value of 18.58 for the 12^th lag from a data sample. Are the data significantly correlated at the lag examined or not? You want to be 95% confident in your answer.

A. Yes. The data are significantly correlated through the 12th lag.
B. No. The data are not significantly correlated through the 12^th lag.

C. No. Only the 12 lag period is not correlated.

D. You cannot tell since the number of sample observations is not provided.

E. The p-value is above .05 so the data is correlated.

8. Sometimes forecasters get lazy or forgetful and do not check the significance of XY data correlations and use the X variable to forecast Y. What is the result of this?

A. Type 2 error
B. Autocorrelation error
C. Type 3 error
D. Type 1 error

9. Do error measures indicate the statistical significance of forecast model variables?

A. Yes. They move in the same direction as statistical significance.
B. Yes. As error measures decrease the variable significance increases.
C. No They indicate only the magnitude of estimate error.
D. No. They indicate only the statistical significance of a forecast or fitted values.

10. In exponential smoothing what is the weight of the alpha coefficient for a time series data observation from the 3^rd previous period if the original alpha value is set at .8?

A. The weight cannot be calculated since the data observation is not given.
B. The weight is zero since the alpha value is set relatively high.
C. .548
D. .0064

11.Given the data series below for variables Y (Monthly Inventory Balance) and X (Monthly Sales) are they significantly correlated at the 95% confidence level and how can you tell?

Ending Inv. Bal. Y		Monthly Sales X
1544		5053
1913		5052
2028		7507
1178		2887
1554		3880
1910		4454
1208		3855
2467		8824
2101		5716

A. Yes. The correlation coefficient is .873 that is greater than .05.
B. Yes. The correlation p-value is .002 which is less than .05.
C. No. The correlation coefficient is above the p-value.
D.No. The correlation p-value is greater than the 95% confidence level.

12. You have forecast the sales for your company for the last 12 months and the forecast residuals are shown below. Are these residuals to be considered random?
Residuals

-24

-348

-892

-62

-378

-489

-342

490

578

198

A. Yes, since the residuals randomly vary in magnitude.
B. Yes since the residuals are positive and negative and vary in magnitude.
C. No, since the residuals are stationary and vary in magnitude.
D. No, since the residuals indicate positive slope.

13. Given the residuals in problem 12 above what is the RMSE for the forecast?

A. -101.0
B. 411.8
C. 169603
D. 220.1

14. Which form of exponential smoothing can result in a na

This includes showing all calculations and explaining why you selected a specific answer for each multiple choice question (i.e. donât just circle the correct answer). I am looking to see how you got the answer, not just that you have the correct answer.

Below is data from the United States Cancer Statistics about the number of news cases of lung cancer in males in the U.S. for 2011 for ages 30 and older.

Table 1: U.S. Population Size and Incidence Cases of Lung Cancer in Males for 2011

Age (Years)	U.S. Male Population	White Population	White Incidence Cases	Black Population	Black Incidence Cases
30-34	10,181,564	7,950,924	88	1,383,650	22
35-39	9,666,162	7,557,263	212	1,271,897	23
40-44	10,363,126	8,259,215	643	1,324,847	132
45-49	10,856,131	8,766,225	2,032	1,373,346	444
50-54	10,976,172	9,004,383	5,128	1,329,551	1,148
55-59	9,733,849	8,101,629	8,607	1,091,030	1,687
60-64	8,466,308	7,183,960	12,340	845,362	2,067
65-69	6,014,777	5,178,255	15,792	539,796	2,077
70-74	4,360,942	3,769,569	16,011	376,129	1,864
75-79	3,204,196	2,807,216	14,319	255,221	1,426
80-84	2,319,839	2,078,071	11,284	154,155	883
85+	1,873,942	1,688,433	7,616	117,267	545
Total	88,017,008	72,345,143	94,072	10,062,251	12,318

3. What is the age-specific incidence rate for lung cancer in white men age 75-79 for 2011?(1 pt)

0.005 per 1000

1.3 per 1000

1.2 per 1000

5.1 per 1000

5.6 per 1000

F. Cannot be calculated from the given information

4. What is the age-specific incidence rate for lung cancer in black men age 75-79 for 2011? (1 pt)

0.005 per 1000

1.3 per 1000

1.2 per 1000

5.1 per 1000

5.6 per 1000

F. Cannot be calculated from the given information

Questions 5 through 7 are based on the information below:

Using the information in Table 1, researchers calculated the crude incidence rates and age-adjusted incidence rates (via the direct method) for both groups.

Table 2: Crude incidence rates and age-adjusted incidence rates for white and black males

White Males		Black Males
Crude Incidence Rate	Age-adjusted Incidence Rate	Crude Incidence Rate	Age-adjusted Incidence Rate
1.3 per 1000	1.2 per 1000	1.2 per 1000	1.5 per 1000

5. True or False, there is likely a difference in the age composition between the white and black males. Explain your answer

6. Based on the information in Table 2, it was reported that there was an increased risk of lung cancer in black males in 2011. (1 pt)

The conclusion is:

Correct, the age-adjusted rate is higher in black males compared to white males

Correct, because both the crude and age-adjusted rates are higher in black males compared to white males

Incorrect, because the incidence rate for white males is actually higher than the incidence rate for black males

7. What type of age-adjusted rate was calculated in table 2? How does it differ from the age-adjusted rate in question 5 in the in-class exercise for age-adjustments? Hint: See slide title: Adjustments for Other Measures of Disease Frequency in the lecture title Adjusted Rates (1 pt)

Question 8 is based on the information given below:

Cause-specific mortality rates for men in 2010 in the U.S. from various types of cancers are shown in the table below:

Cause-Specific Mortality Rates

(per 100,000 Men)

Location of the Cancer

in the Body White Asian

Pancreas 13.2 5.7

Prostate 19.1 2.5

Lung 62.3 18.5

Skin 4.9 0.3

8. The inference that White men in the U.S. are at higher risk of death due to cancer of the pancreas, prostate, lung, and skin compared to Asian men in the U.S. is

A. correct

B. incorrect because of failure to determine cause-specific mortality rates

incorrect because proportionate mortality alone does not give an estimate of risk

D. incorrect because of failure to adjust for differences in the age composition of the two populations

E. incorrect because counts were used when cause-specific mortality rates were needed

9. In January 1996, a team of epidemiologists identified a sample of 4,500 men, 65-74 years of age, for a study of prostate cancer. Tests indicated that 315 of the men already had prostate cancer and, therefore, were not at risk. The rest of the men were followed prospectively for five years to determine the incidence rate of prostate cancer in the sample. By the end of the five years of follow-up 156 of the men had developed prostate cancer. What is the incidence rate of prostate cancer in this group?

10. An epidemiologic investigation that started on January 1, 2011, identified a population of 1,000 individuals. At the start of the study 4 were found to have the disease. During the year of study, 6 new cases were found; thus a total of 10 cases were identified. Among those 10 cases, 6 deaths occurred during the year. What was the prevalence of the disease during the 1-year study?

pinkhornet564

EEMB 146 Lecture Notes - Lecture 5: Sampling Distribution, Standard Error, Statistical Parameter

Document Summary

Get access

Related Documents

EEMB 146 Lecture Notes - Lecture 1: Biostatistics, Statistical Parameter, Sampling Error

BIOL 300 Chapter Notes - Chapter 4: Sampling Distribution, Confidence Interval, Statistical Parameter

BIOL 2060 Lecture 4: Chapter 4

Related Questions