Question

A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights​ (in centimeters) of randomly selected presidents along with the heights of their main opponents. Complete parts​ (a) and​ (b) below.

Identify the test statistic.

t=

Identify the​ P-value.

​P-value =

What is the conclusion based on the hypothesis​ test?

Since the​ P-value is_____ the significance​ level ______the null hypothesis. There _____sufficient evidence to support the claim that presidents tend to be taller than their opponents.

b. Construct the confidence interval that could be used for the hypothesis test described in part​ (a). What feature of the confidence interval leads to the same conclusion reached in part​ (a)?

The confidence interval is ____ cm<μd<____ cm.

What feature of the confidence interval leads to the same conclusion reached in part​ (a)?

Since the confidence interval contains ______, ______ the null hypothesis.

Height (cm) of President   Height (cm) of Main Opponent
179   173
171   186
177   174
178   168
187   190
180   172

Answer 1

Solution-:

By using R-Software:

(a)
> #Hypothesis:
> #Ho:mud=0 V/s mud > 0
> x=c(179,171,177,178,187,180);x
[1] 179 171 177 178 187 180
> y=c(173,186,174,168,190,172);y
[1] 173 186 174 168 190 172
> t.test(x,y,paired=T,)

Paired t-test

data: x and y
t = 0.39643, df = 5, p-value = 0.3541
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
-6.124413 Inf
sample estimates:
mean of the differences
1.5
Fom this output we get,

Decision Rule: If P-value <0.05(alpha), Reject , at Los Otherwise accept it.
Interpretation: p-value=0.3541>0.05, fail to reject  .

i.e. Since, the​ P-value =0.3541 is  greater than the significance​ level =0.05 hence, fail to reject the null hypothesis. Conclusion: There not sufficient evidence to support the claim that presidents tend to be taller than their opponents.

(b) 95% confidence interval (-6.124413, Inf) includes 0 hence, fail to reject  .

  The confidence interval is -6.124413 cm<μd< Inf.

the confidence interval leads to the same conclusion reached in part​ (a)

Since, the confidence interval contains -6.124413, Inf hence, fail to reject null hypothesis.