Question

V. Hypothesis test and confidence intervals.

1. A sample (n) is taken at random from a population and produces (the sample)
A

= 1100, S = 200. Try the following hypothesis: If we assume the following size of
sample n = 36
a, Is there evidence that the average μx is less than 1200? α = .10

H0: μx = 1200
H1: μx <1200

* For the previous test (item a) estimate the p-value
* Determine the power of the previous hypothesis test. (1-β)
* Estimate 95% confidence interval for the true average value.

SAW. Linear Regression and Correlation.

The following n = 5 data were collected for a linear regression study for two variables.

26 24 144 158 136
ΣX ΣY ΣXY ΣX ^ 2 ΣY ^ 2

_____ X Y
2 2
Four. Five
5 3
7 7
8 7

to. Develop a graph X, Y (Scatter diagram)
* Compute the linear regression equation
* If x = 10, what value would you estimate for "y" the linear regression equation?
* Test the following hypothesis for the previously calculated linear regression slope:
       Use an alpha of α = .10 MSE = 1.544
  
Ho: β = 0 There is no linear relationship between X and Y
Ha: β> 0 There is some positive linear relationship between X and Y

* Compute the correlation coefficient r
* Test the following hypothesis for the previously calculated correlation coefficient:
       Use an alpha of α = .01
  
Ho: ρ = 0 There is no relationship between X and Y
Ha: ρ> 0 There is some positive relationship between X and Y

* Compute the correlation coefficient r
* Test the following hypothesis for the previously calculated correlation coefficient:
       Use an alpha of α = .01
  
Ho: ρ = 0 There is no relationship between X and Y
Ha: ρ> 0 There is some positive relationship between X and Y

VI1. Goodness of fit test for the Poisson distribution
We want to test the following hypothesis for a given study.

Ho The cars parked in the houses follow a Poisson distribution with λ = 1.3.
Ha Cars parked in houses Do not follow a Poisson distribution with λ = 1.3.

Use an α = .10 750 observations were taken. The data of a study are the following:

Number of cars Frequency   λ=1.3
                      P(x)
0 170                 .2725
1 270                 .3543
2 200                 .2303
3 o mas 110                 .1429

Answer 1

V. Hypothesis test and confidence intervals.

The hypotheses are

Ho Hx 1200 H1 : μ、〈 1200

Given the sample size
n=36
and sample mean
x = 1100
, sample standard deviation
s = 200
. Degrees of freedom is
df = n-1=35
.

The test statistic is

X- 1200 1100 - 1200 200 V36 t3

The P-value is

P-value = P(T <-3) P-value 0.0025

The power of the test is

Power= 1-3 = P( reject H0| H1 true) Power = 에 tan-1 + s/ ) 1200 -1100 Power= ΦΤ1-1.306212 + 200/V36 Power = Φ7( 1.693788) Power 0.95

The two sided confidence interval for population mean based on the sample data is

(1-0) 100%

1-a2,n-1

The 95% confidence interval for the true average value is

200 1100 t1-0.1/2,35 36 (1043.681,1156.319)