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

Answer:

-0.861,0.195

Step-by-step 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 = $\frac{115}{149} =0.7718$

$q=1-p = 0.2282$

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

(left tailed test at 5% significance level)

If H0 is true, std error = $\sqrt{\frac{0.8*0.2}{149} } =0.033$

a) Z statistic = p diff/std error  

=$\frac{0.7718-0.80}{0.033} \\=-0.861$

b) p value = 0.195