EC272 Final

two-sided test

HO: MU = 5

HA: MU =/ 5

Lower tailed test

HO: MU > 5

HA: MU < 5

Upper Tailed Test

HO: MU < 5

HA: MU > 5

Type 1 Error

Rejecting null hypothesis when it is true

Type 2 Error

failing to reject a false null hypothesis

a true alternative hypothesis is mistakenly rejected

degrees of freedom

n-1

test statistic

result of z-score equation

p-value

number from table after getting test statistic

reduce the price

lower tailed test

HO: MU > X

increase the price

upper tailed test

HO: MU < X

when sigma is unknown

get z score using s instead

then find degrees of freedom, p-value (ex. 05) and find t value

z score for population proportion

pbar-p / p (1-p) / n

p-value approach

comparing value found from chart to alpha

ex. (0.0409 < .05)

critical approach

comparing test statistic (z score answer) to critical value of alpha

ex. 1.67 < 2.33 (a=0.1)

Critical value for 0.05

1.645

Critical value for 0.01

2.33

Critical value for .025

1.96

Critical value for .005

2.575

Critical value for 0.10

0.5398

When trying to find a value on a table that I don't know (ex. a=.02)

Find value closest to .02 on the negative z score table and then see what number makes it

point estimator

xbar1-xbar2

interval estimate

xbar1 -xbar2 +- Za/2 SQRT sigma/n1 + sigma2/n2

Reject the null

p-value is less than alpha

Fail to reject the null

p-value is greater than alpha

SST

total sum of squares

SSR

sum of squares due to regression

SSE

sum of squares due to error

R2

coefficient of determination

Mean Square Error (MSE)

S2

a regression model in which more than one independent variable is used to predict the dependent variable is called

a multiple regression equation

the term used the describe the case when the independent variable in a multiple regression equation are correlated

Multicollinearity

A multiple regression model has

more than one independent variable

a measure of the goodness of fit of the estimated multiple regression equation

multiple coefficient of determination

The adjusted multiple coefficient of determination accounts for

the number of independent variables in the model

the multiple coefficient of determination is computed by

R2 = dividing SSR by SST

Relationship between SST SSR SSE

SST = SSR + SSE

dummy variable

a variable that takes on one of two values (usually one or zero)

Standard error equation

σ/√n

A value is significant if

the p-value is less than alpha.

Historical method

-leave week 1 blank and move sale # to week 2 forecast

-add all previous sales and divide by the #of sales

ex.

17+22/2=19

17+22+19/3=19

17+22+19+23/4=28

Moving average method

-leave blank amount of weeks it says

-add all previously skipped sales #s and divide by the moving avg number

ex.

3 week moving avg

17+21+19/3=19

21+19+23/3=21

19+23+18/3=20

Linear trend projection

Week (T) Sales (y)

Naive method

-use all T (sales) values as forecast in order

-leave the first week blank

absolute % error

(FT (forecast) - T (original values) / T) * 100

MSE

mean square error

MAE

mean absolute error

MAPE

Mean Absolute Percentage Error

Absolute error

Forecast value - True value

Squared error

Square all absolute error values

In logistic regression,

the dependent variable only assumes two discrete values

testing significance of the model, the critical value of F at 95% confidence is

n-p-1

(P) Regression

amount of x variables in the equation

F-value greater than 4.0

usually significant

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the...

central limit theorem

A simple random sample of 64 observations was taken from a large population. The sample mean and the standard deviation were determined to be 320 and 120 respectively. The standard error of the mean is..

120/sqrt 64 = 15

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the sample mean will be larger than 82 is....

82-80 =2

z = 2

look at negative side of the chart

= 0.0228

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the mean from that sample will be between 183 and 186 is...

0.1359

It is known that the variance of a population equals 1,936. A random sample of 121 has been taken from the population. There is a .95 probability that the sample mean will provide a margin of error of....

0.95 => = 0.05

a/2 = 0.025

=> E = 1.96 (44/√121)

7.84

The sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is....

n = (1.96 * 11/2)^2

117

The following random sample from a population whose values were normally distributed was collected. 10, 12, 18, 16. The 80% confidence interval for μ is...

11.009 to 16.991

In a random sample of 114 observations, pbar= 0.6. The 95% confidence interval for P is..

0.52 to 0.68

In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is

0.071 to 0.0129

A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 95% confidence interval for μ is

180 +- Z .95/2 , 75/sqrt 225

180 +- 8.035

170.2 to 189.8

a random sample of 49 statistics examinations was taken. the average score, in the sample, was 84 with a variance of 12.25. The 95% confidence interval for the average examination score of the population of the examination is...

83.00 to 85.00

standard error of the difference between 2 means..

SE = SQRT sigma1^2/n1 sigma2^2/n2

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes...

Test statistic is = 2.00

p-value is between = 0.1 and .025

95% confidence, mean is = significantly greater than 3

For a two tailed test at 86.12% confidence, Z=

1 - .8612 =0.1388

= 0.1388 /2 = 0.0694

1.48

A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%

Test stat = 1.25

p-value = 0.1056

At 95% confidence, the pop. proportion favoring Candidate A = is not significantly greater than 80%

Type 2 error is committed when

a true alternative hypothesis is mistakenly rejected

Confidence Interval Formula

Xbar +/- Za/2 , sigma /sqrt n

margin of error equation

Z a/2 , sigma / sqrt n