Question

Indicate whether the following analysis involves a statistical test. If it does involve a statistical test, state the population parameter(s) of interest and the null and alternative hypotheses.

a. Testing 100 right-handed participants on the reaction time of their left and right hands to determine if there is evidence for the claim that the right hand reacts faster than the left.
b. Testing 100 right-handed participants on the reaction time of their left and right hands to determine if there is evidence for the claim that the right hand reacts faster than the left.
c. Polling 1000 people in a large community to determine if there is evidence for the claim that the percentage of people in the community living in a mobile home is greater then 10%.

Answer 1

a

Yes it involves a statistical test

The population parameter(s) of interest is

The sample size is n = 100

The average reaction time of the right hands for the right-handed participants
`\mu_R`

The average reaction time of the left hands for the left-handed participants
`\mu_L`

The null hypothesis is
`H_o : \mu_R = \mu_L`,

The alternative hypothesis is
`H_a: \mu_R < \mu_L`

b

Yes it involves a statistical test

The population parameter(s) of interest is

The sample size is n = 100

The average reaction time of the right hands for the right-handed participants
`\mu_R`

The average reaction time of the left hands for the left-handed participants
`\mu_L`

The null hypothesis is
`H_o : \mu_R = \mu_L`,

The alternative hypothesis is
`H_a: \mu_R < \mu_L`

c

Yes it involves a statistical test

The population parameter(s) of interest is

The percentage of people in the community living in a mobile home is denoted with p

The sample size is n = 1000

The null hypothesis is
`H_o : p =10\% = 0.01`,

The alternative hypothesis is
`H_a: p >10\% = 0.01`

Explanation:

Considering the first statement

Testing 100 right-handed participants on the reaction time of their left and right hands to determine if there is evidence for the claim that the right hand reacts faster than the left.

Yes, the analysis does involve a statistical test.

The null hypothesis is
`H_o : \mu_R = \mu_L`,

The alternative hypothesis is
`H_a: \mu_R < \mu_L`

Here
`\mu_R` is the average reaction time of the right hands for the right-handed participants

and
`\mu_L` is the average reaction time of the left hands for the left-handed participants

Considering third statement

Polling 1000 people in a large community to determine if there is evidence for the claim that the percentage of people in the community living in a mobile home is greater then 10%.

The percentage of people in the community living in a mobile home is denoted with p

The sample size is n = 1000

The null hypothesis is
`H_o : p =10\% = 0.01`,

The alternative hypothesis is
`H_a: p >10\% = 0.01`