Question

For this problem, solve the problems by answering a) state the claim using a sentence, b) Ho H1 and place the claim with either one of the two, c) Test statistic, show and label the formula you use, d) find critical value(s), and reject Ho or fail to reject Ho. You may use p-value. e) Write a formal conclusion and final statement (Please show all work and label answer a,b,c,d,e)

The Pew Research Center claims that at least 54% of Californians favor a tax increase to pay for new schools. You decide to test this claim and ask a random sample of 80 citizens and 36 favor the new tax. Use a=0.01 to test this claim.

a)

b)

c)

d)

e)

Answer 1

Answer)

A)

The population proportion is greater than or equal to 0.54

B)

Ho : P >= 0.54 (claim)

H1 : P < 0.54

C)

N = 80

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 43.2

N*(1-p) = 36.8

Both the conditions are met so we can use standard normal z table to estimate the P-Value

Test statistics z = (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed P = 36/80

Claimed P = 0.54

N = 80.

After substitution

Test statistics z = -1.62

D)

From z table, P(z<-2.33) = 0.01

Rejection region is reject Ho

If test statistics is less than -2.33

Since -1.62 is not less than -2.33

We fail to reject the null hypothesis Ho

E)

We have enough evidence to support the claim that at least 54% of Californians favor a tax increase to pay for new schools.