Question

Researchers suspect that myopia, or nearsightedness, is becoming more common over time. A study from the year 2010 showed 123 cases of myopia in 400 randomly selected people. Another study from the year 2019 showed 228 cases in 600 randomly selected people. We are going to do a hypothesis test to see if p1 = the proportion of people who have myopia in 2019 is equal to p2 = proportion of people who have myopia in 2010 at the 0.05 significance level.

null and alternative hypothesis ?
a. H0:P1=P2; Ha：P1≥P2
b. H0:P1=P2; Ha：P1≠P2
c. H0:P1≠P2; Ha：P1=P2
d. H0:P1≥P2; Ha：P1≠P2

Answer 1

• < 0.5 \leqslant pvalue < 0.10[/tex]
• answer C on khan academy

Answer 2

We want to test if the if p1 = the proportion of people who have myopia in 2019 is equal to p2 = proportion of people who have myopia in 2010 (alternative hypothesis) , then the system of hypothesis are:

Null hypothesis:
`p_1 = p_2`

Alternative hypothesis:
`p_1 = p_2`

And the best option would be:

b. H0:P1=P2; Ha：P1≠P2

Explanation:

For this case we have the following info given:

`X_1 = 228` the myopia cases in 2019

`n_1= 600` the sample size in 2019

`\hat p_1= (228)/(600)= 0.38` estimated proportion of myopia cases in 2019

`X_2 = 123` the myopia cases in 2010

`n_2= 400` the sample size in 2010

`\hat p_2= (123)/(400)= 0.3075` estimated proportion of myopia cases in 2010

And we want to test if the if p1 = the proportion of people who have myopia in 2019 is equal to p2 = proportion of people who have myopia in 2010 (alternative hypothesis) , then the system of hypothesis are:

Null hypothesis:
`p_1 = p_2`

Alternative hypothesis:
`p_1 = p_2`

And the best option would be:

b. H0:P1=P2; Ha：P1≠P2

And we can conduct a two sample z proportion test in order to verify the hypothesis.