Question

Dentists make many people nervous. To see whether such nervousness elevates blood pressure, the blood pressure and pulse rates of 60 subjects were measured in a dental setting and in a medical setting. For each subject, the difference (dental-setting blood pressure minus medical-setting blood pressure) was calculated. The analogous differences were also calculated for pulse rates. Summary data are given below.

	Mean Difference	Standard Deviation of Differences
Systolic Blood Pressure	4.43	8.77
Pulse (beats/min)	−1.30	8.84

(a)

Do the data strongly suggest that true mean blood pressure is greater in a dental setting than in a medical setting? Use a level 0.01 test. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We do not reject H₀. We have convincing evidence that the mean blood pressure is greater in a dental setting than in a medical setting.We reject H₀. We have convincing evidence that the mean blood pressure is greater in a dental setting than in a medical setting.    We reject H₀. We do not have convincing evidence that the mean blood pressure is greater in a dental setting than in a medical setting.We do not reject H₀. We do not have convincing evidence that the mean blood pressure is greater in a dental setting than in a medical setting.

(b)

Is there sufficient evidence to indicate that true mean pulse rate in a dental setting differs from the true mean pulse rate in a medical setting? Use a significance level of 0.05. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We do not reject H₀. We have convincing evidence that the mean pulse rate in a dental setting differs from the mean pulse rate in a medical setting.We reject H₀. We have convincing evidence that the mean pulse rate in a dental setting differs from the mean pulse rate in a medical setting.    We reject H₀. We do not have convincing evidence that the mean pulse rate in a dental setting differs from the mean pulse rate in a medical setting.We do not reject H₀. We do not have convincing evidence that the mean pulse rate in a dental setting differs from the mean pulse rate in a medical setting.

Answer 1

Here the difference (dental-setting blood pressure minus medical-setting blood pressure) was calculated.

We want to test whether data strongly suggest that true mean blood pressure is greater in a dental setting than in a medical setting

Let be true mean of difference between  blood pressure in a dental setting and in a medical setting.

The null hypothesis is given as

and the alternative hypothesis is given as

Let d = the difference between dental-setting blood pressure minus medical-setting blood pressure.

Mean difference

4.43

Standard Deviation of Differences

s=  8.77

Total subject

n= 60

The test statistic is given as

= 3.912729

~ = 3.91

df = n-1

=60-1

= 59

p-value is given as( as this is one tailed test)

P[ t59 < 3.91 ] = 0.000119

~0

Since p-value < = 0.01( level of significance)

We reject H0. We have convincing evidence that the mean blood pressure is greater in a dental setting than in a medical setting.

B)

Here we have to test whether true mean pulse rate in a dental setting differs from the true mean pulse rate in a medical setting.

Let be true mean difference betweenpulse rate in a dental setting and in a medical setting.

The null hypothesis is given as

and the alternative hypothesis is given as

Let d = the difference between dental-setting pulse rate minus medical-setting pulse rate

Mean difference

−1.30

s = 8.84

The test statistic is given as

=  -1.139113

~ = -1.14

Degree of freedom df = n-1

= 60-1= 59

Obtaining the p-value

= 0.129

Since p -value = 0.129> = 0.05

We failed to reject null hypothesis.

We do not reject H0. We do not have convincing evidence that the mean pulse rate in a dental setting differs from the mean pulse rate in a medical setting.