SOCECOL 10 Lecture Notes - Lecture 8: Statistical Inference, Null Hypothesis, Intelligence Quotient

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amethystcockroach109

1 Apr 2017

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P-value: probability of sample difference if null is true: how confident we can be about our conclusions. The smaller the p-value, the better (the more confidence we can have) P-value tells us what are the chances that we are wrong: probability of obtaining a correlation as large as we have obtained in our sample if the null hypothesis is actually true. Null hypothesis of a correlation is that the r value is 0: says there are no differences between groups. * don"t say significant unless you did an inferential test to find p-value* If your results were significant at p<0. 001, the probability that the results occurred by chance alone is less than 1 in 1000. In the slide: 68% fall within one sd of the mean, 95% fall within two sds of the mean. Jane has scored 132 on the iq test. The mean is 100 and the sd is 16.

Related Questions

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

Hi - could someone please assist me with this question? It's giving me nightmares......thanks

Historically, the average waiting time spent in a queue on Friday afternoon at a bank's city branch was 10 minutes. To determine whether their new multi-queuing system constitutes an improvement, a random sample of 15 customers was taken and their waiting time recorded. The results are in the X1 column of the datafile P14.12. Assume the distribution of waiting times is normally distributed.

1. State the direction of the alternative hypothesis used to test whether there is an improvement in average waiting time. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as required in the box.

2. Calculate the test statistic correct to three decimal places (hint: use Descriptive Statistics to calculated the standard deviation and sample mean).

3. Use Kaddstat to determine the p-value for the test correct to four decimal places.

4. Is the null hypothesis rejected for this test if a 10% level of significance is used? Type yes or no.

5. Disregarding your answer for 4, if the null hypothesis was rejected, could we conclude that the average waiting time has improved with the new queuing system? Type yes or no.

DATA FILE

135

You work for Segway, in the sales division of the Drift W1 (which are basically motorized roller skates). Youâve traveled into the future (since they arenât available yet) and collected data on monthly sales (S) and the price of the Drift W1 (P), both in dollars, as well as the daily average summer temperature in your most popular market (T) in degrees Fahrenheit. You estimate the following regression model: S=a+bP+cT In your regressions, you usually look for a 10%-or-better level of confidence.

The expected sign of

Select one:

a. b is negative and c is positive.

b. b is negative and c is negative.

c. b is positive and c is positive.

d. b is positive and c is negative.

Your regression yields the following results:

Dep. Var.: S
Adj. R-square 0.820

Variable	Coefficient	Standard Error	t-stat	P-value
Intercept	1936	309	6.259	0.00153
P	-4.71	0.81	-5.816	0.00212
T	6.57	3.50	1.879	0.11902

The estimated coefficient for aa (intercept) suggests that

Select one:

a. If PP and TT are zero, we could still expect about $1,936 in sales per month.

b. aa cannot be interpreted with confidence since its parameter estimate is not statistically significant.

c. Sales will range between $309 and $1,936 per month, but not outside those limits.

d. Sales will be $1,936 per month when PP and TT are at their optimal values.

The estimated coefficient for bb (price of the Drift W1) suggests that

Select one:

a. a $1 increase in the price of the Drift W1 is associated with a decrease of monthly sales of $4.71.

b. monthly sales will increase by $5.816 if the price of the Drift W1 decreases by $4.71.

c. a one-dollar increase in price is associated with an increase in monthly sales of 4.71 units.

d. when price is close to $212, then consumers will demand one more unit per month if price drops by $4.71.

The estimated coefficient for cc (daily average summer temperature) suggests that

Select one:

a. a one-degree increase in temperature is associated with a $3.50 increase in monthly sales.

b. temperature has a more important effect on our sales than does the price of our units, since c>bc>b.

c. a one-degree increase in temperature is associated with a $119.02 increase in price.

d. a one-degree increase in temperature is associated with a $6.57 increase in monthly sales.

The price of the Drift W1 has a statistically significant effect on our sales.

Select one:

True

False

Daily average summer temperature affects the sales of the Drift W1 in a statistically significant way.

Select one:

True

False

What portion of the total variation in sales of the Drift W1 remains unexplained?

Select one:

a. 0.872, or 87.2%

b. 0.180, or 18.0%

c. 0.00153, or 0.153%

d. 0.051, or 5.1%

Segway is considering selling the Drift W1 in a new city, where the average daily summer temperature is 73Â°, for a price of $320. What level of sales would you expect in this new city (rounded to the nearest dollar)?

Answer:

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SOCECOL 10 Lecture Notes - Lecture 8: Statistical Inference, Null Hypothesis, Intelligence Quotient

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