How to identify the Ho and the Ha? what are the keywords to look for to help sol

Question

How to identify the Ho and the Ha?

what are the keywords to look for to help solve such problem?

how to tell which is the n, 81 or 400?

On excel for proportion with no sigma which function is used to solve test stat, Critical Value, P-value?

According to the federal government, 24% of workers covered by their company's health care plan were not required to contribute to the premium (Statistical Abstract of the United States: 2006). A recent study found that 81 out of 400 workers sampled were not required to contribute to their company's health care plan.

Develop hypotheses that can be used to test whether the percent of workers not required to contribute to their company's health care plan has declined.

H0:
Ha:

What is a point estimate of the proportion of workers who are not required to contribute to their company's health care plan (to 4 decimals)?

Has a statistically significant decline occurred in the proportion of workers who are not required to contribute to their company's health care plan? Use  = 05.

Calculate the value of the test statistic (to 2 decimals).


What is the p-value (to 4 decimals)?


What is your conclusion?

Explanation / Answer

H0: p=0.24

Ha: p<0.24

point estimate of the proportion phat=x/n=81/400 =0.2025

here std error =(p(1-p)/n)1/2 =0.0214

hence test stat t=(phat-p)/std error =(0.0214-0.24)/0.0214 =-1.756

p value fro above =0.0395

as po vlaue is less then 0.05 level, hence we reject null hypothesis/

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