Write the symbolic version of the claim, the null hypothesis and the alternative

Question

Write the symbolic version of the claim, the null hypothesis and the alternative hypothesis. Clearly label each answer. Claim: At least 75% of all households have participated in some type of recycling program. Using a sample of 500 randomly selected households, the claim, "At least 75% of all households have participated in some type of recycling program", is going to be tested. Which distribution (normal, t, or chi-square) should be used? Why? lf a null hypothesis is rejected at the 0.05 level of significance, is it a certainty that it will also be rejected at the 0.01 level of significance? Why?

Explanation / Answer

1) h0:mu=75%

Ha:mu >75%

2)normal

because n=500 its a large number

3)    If the p-value is less than 0.05, we reject the null hypothesis(not significant)

there is no certainity that it will also reject at 0.01

because p value may lie between 0.01 and 0.05

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