STATS ALLEY
It is known that the population variance equals 484. With 0.95 probability, the minimum sample that needs to be take if the desired margin or error is 5 or less is
.05/2=0.25 1-0.25=.9750 Look up .9750 on Z=1.96 Square root 484=22 (1.96*22/5)^2=74.37 =75
For a one tailed test (upper tail) a sample size of 26 at 90% confidence, T=
.10 26-1=25 DF Look up on T table
If an interval estimate is said to be constructed at the 90% confidence level the confidence coefficient would be
.90
For a two tailed test at 86.12% confidence, the critical values of Z
1-.8612=.1388 .1388/2=.0694 =1.48
The T value for a 95% confidence interval estimation with 24 degrees of freedom
1. 1-.95=.05 2. .05/2=.025 3. Look up .025 with 24 degrees=2.064
The z value for a 97.8% confidence interval estimate is
1. 1-.978=.022 2. .022/2=.0110 3. Look up Z = 2.29
A regression analysis between sales (in 1000) and price (in dollars) resulted in the following equation y=60-8x The above equation implies that an
1. 60-8(x+1)-60-8x 2. 60-8x-8-60-8x=-8 3. -8(1000)=8000 4. increase of 1$ in price is associated with a decrease of 8000 in sales
From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence the margin of error is
1. Square root 900=30 2. N=225 3. 1-.95=.05 4..05/2=.025 5. Z-value= 1.96 6. 1.96*(30/Squareroot225) 7.3.92
Regression analysis was applied between sales data (y in 1000) and advertising data (x in 100) and the following information was obtained y=12+1.8x If advertising is 3000 the the point estimate for sales in dollars
12+1.8(30)=66 in thousands
In Hypothesis testing if the NULL hypothesis has been rejected when the ALTERNATIVE hypothesis is true
Correct decision has been made
The average monthly rent for a one bedroom apartment is chattanooga has been 700. Because of the downturn in the marketis is believed there is a decrease the correct hypothesis is
Ho=U≥700 Ha=u<700
The probability of committing a Type 1 error when the null hypotheses is true is
Level of Significance
In a regression and correlation analysis if r^2=1
SSE must be equal to zero
If r^2=1 then
SSR=SST
When s is used to estimate (omega) the margin of error is computed by using
T-Distribution
If a null hypothesis is rejected at 95% confidence it
Will always be rejected at 90% confidence
In the following estimated regression equation y=bo+b1x
b1 is the slope bo is the yintercept
Type 2 Error is denoted by
by β
If the coefficient of determination is a positive value, then the coefficient of correlation
can be either negative or positive
The coefficient of determination
can not be negative
The value added and subtracted from a point estimate in order to develop an interval estimate of the population of the population parameter is known as the
margin of error
If the coefficient of correlation is -0.4 then the slope of the regression line
must also be negative must be the same sign
When the p-value is used for hypothesis testing, the null hypothesis is rejected if
p-value≥α
In regression analysis the dependent variable
the variable that is being predicted
In regression analysis the independent variable
used to predict the dependent variable
Type 1 error (alpha)
α