Question

HW3.csv 202 Swearing Not Swearing 182. 180 | 165 250 200 95 278 200 164 230 150 110 | 241 1 189 130 147 209 225 256 239 165 | 189 190 | 210 265 239 202 185 147 291 132 | 152 130 17 166)

Please use program "R" to answer these questions.

1. Conduct an unpaired t-test (yes! again) with the same dataset assuming two independent samples with equal variance. Report the P value and the confidence interval for the difference between means.

2. Conduct a linear regression analysis equivalent to the unpaired t-test (see page 361 in the book). Report the slope with its confidence interval, and the P value based on the F ratio test. Explain the results. NOTE: the p-value should be identical to the one obtained in part “c.”

Answer 1

a. R code:

x=c(202,180,250,101,90,265,278,241,189,130,147,209,225,256,239,265,291,132,152,77)
y=c(182,165,200,95,69,200,164,230,150,110,165,189,190,210,239,202,185,147,130,66)
t.test(x, y, alternative = "two.sided", var.equal=TRUE,paired=FALSE)

Output:

       Two Sample t-test

data: x and y
t = 1.7034, df = 38, p-value = 0.09667
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-5.946296 69.046296
sample estimates:
mean of x mean of y
   195.95    164.40

p-value=0.09667

95 percent confidence interval for the difference between means:
(-5.946296, 69.046296)

Here x=observations come from Swearing, y=observations come from not Swearing

b.

R code:

y1=c(202,180,250,101,90,265,278,241,189,130,147,209,225,256,239,265,291,132,152,77)
y2=c(182,165,200,95,69,200,164,230,150,110,165,189,190,210,239,202,185,147,130,66)
y=c(y1,y2)
x=c(1:20*0+1,1:20*0)
Model=lm(y~x)
summary(Model)
anova(Model)

Output:

Call:
lm(formula = y ~ x)

Residuals:
    Min      1Q Median      3Q     Max
-118.95 -45.20    9.55   43.55   95.05

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)   164.40      13.10 12.552 4.32e-15 ***
x              31.55      18.52   1.703   0.0967 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 58.57 on 38 degrees of freedom
Multiple R-squared: 0.07094,   Adjusted R-squared: 0.04649
F-statistic: 2.901 on 1 and 38 DF, p-value: 0.09667

Analysis of Variance Table

Response: y
          Df Sum Sq Mean Sq F value Pr(>F)
x          1   9954 9954.0 2.9014 0.09667 .
Residuals 38 130368 3430.7                
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Slope= 31.55,

95% CI for Slope=(31.55-t_0.025,38*18.52, 31.55+t_0.025,38*18.52)=(-5.9419, 69.0419) where, = 2.0244

p-value=0.09667.

Here x=1 if observation come from Swearing and x=0 if observation come from not Swearing.

Since p-value>0.05 so there is insignificant difference between two population means.