Sampling Distributions for Means Question 3

From a random sample of 50 people, sitting pulse rates and standing pulse rates were measured for each person. A coin was flipped to determine whether the sitting or the standing pulse rate would be measured first. Let $\mu_{sitting}$ represent the mean sitting pulse rate in the population, $\mu_{standing}$ represent the mean standing rate in the population, and $\mu_d$ represent the mean of the differences between the sitting and standing (sitting $-$ standing) pulse rates in the population. Which of the following represents an appropriate test and hypotheses to determine if there is a difference in mean pulse rates between sitting and standing in the population?

A two-sample

t

-test with

H_0 : \mu_{sitting} = \mu_{standing}

and

H_a : \mu_{sitting} \neq \mu_{standing}

A two-sample

z

-test with

H_0 : \mu_{sitting} = \mu_{standing}

and

H_a : \mu_{sitting} \neq \mu_{standing}

A matched-pairs

t

-test with

H_0 : \mu_d = 0

and

H_a : \mu_d \neq 0

A matched-pairs

t

-test with

H_0 : \mu_d = 0

and

H_a : \mu_d \lt 0

Approach

A matched-pairs $t$ -test is appropriate since each individual participates in both sitting and standing pulse rate trials.

The null hypothesis is that there is no difference between the mean pulse rates. The alternative should be that there is a significant difference between the pulse rates.