Question

Spam: Larry claims that more than a quarter of all his email is spam. In a random sample of 80 of his emails, 26 of them are spam. Test his claim at the 0.05 significance level.

(a) What is the sample proportion of spam in his email? Round your answer to 3 decimal places.
p̂ =  

(b) What is the test statistic? Round your answer to 2 decimal places.
z =  

(c) What is the P-value of the test statistic? Round your answer to 4 decimal places.
P-value =   

(d) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀     

(e) Choose the appropriate concluding statement.

The data supports the claim that more than a quarter of all Larry's email is spam.

There is not enough data to support the claim that more than a quarter of all Larry's email is spam.     

We reject the claim that more than a quarter of all Larry's email is spam.

We have proven that more than a quarter of all Larry's email is spam.

Answer 1

Ans:

a)

sample proportion of spam in his email,p-hat=26/80=0.325

b)

z=(0.325-0.25)/SQRT(0.25*(1-0.25)/80)

z=1.55

c)

p-value=P(z>1.55)=0.0606

d)

As,p-value>0.05,fail to reject H₀     

e)

There is not enough data to support the claim that more than a quarter of all Larry's email is spam