Question

Please note that this math problem has not just one, but TWO answers.

The government reports that 80% of adolescents do not do enough aerobic physical activity to meet the guidelines for youth. A local college thinks that this is not true and decides to collect a random sample of 149 adolescents. They found that 115 did not get enough aerobic physical activity.


Conduct a hypothesis test using a significance value of .05 (alpha = .05). Round ALL answers to 4 decimal places.


(a) The z-value for this is z = ?????


(b) The p-value is: ????? (leave your answer as a decimal)


????? = unsolved answer

Answer 1

-0.861,0.195

Explanation:

Population proportion = the proportion reported by the Govt. for adolescents do not do enough aerobic physical activity to meet the guidelines for youth.

= 0.80

Sample size = 149

Sample favourable =115

Sample proportion =
`(115)/(149) =0.7718`

`q=1-p = 0.2282\\`

`H_0: p = 0.80\\H_a: p<0.80`

(left tailed test at 5% significance level)

If H0 is true, std error =
`\sqrt{(0.8*0.2)/(149) } =0.033`

a) Z statistic = p diff/std error

=
`(0.7718-0.80)/(0.033) \\=<strong>-0.861</strong>`

b) p value = 0.195