stats module 6 homework question 12 urgent help please I am so confused

Question

A company creates wooden furniture to be sold at various retailers. This company claims that only 2.24% of their furniture are defective in some manner. Monica would like to test this claim to see if the actual percentage of furniture that is defective is different than the company claims, using α = 0.025. She takes a sample of 1065 pieces of furniture, and observes that 78 of these furniture pieces are defective. Assume a normal sampling distribution.

(a) What are the null and alternative hypotheses?

H₀: pμp1 - p2μ1 - μ2 <≠>= 0.0224 or 0.0732

H_A: pμp1 - p2μ1 - μ2 =≤≥<≠> 0.0224 or 0.0732

(b) What is the test statistic? (Round your answer to 2 decimal places, if needed.)

(c) Using the statistical table, what is the p-value? (Round your answer to 4 decimal places, if needed.)

(d) Based on the p-value, Monica should  reject fail to reject the null hypothesis.

(e) This data  provides does not provide sufficient evidence to conclude that the actual percentage of furniture that is defective is different than the company claims.

Answer 1

Hi Faith,

a. Neither option is correct. This is a one-proportion test, not two proportion, and you were given no information about direction, so you must assume alternative is "not equal to."

H0 : p = 0.0224

HA: p not equal to 0.0224

b. z= (p^-p0)/sqrt(p0q0/n)

p^= sample proportion = 78/1065 = 0.073

p0 = hypothesized population proportion = 0.0224

q0 = 1 - p0 = 1 -0.073 = 0.927

n = sample size = 1065

z= (0.073 - 0.0224) / sqrt ((0.0224*0.927)/1065)

z = 11.46

c. 11.46 will not even appear on z-table, so:

p = 0.0000 (Note p is not actually 0, but 0.0000 is correct to four decimal places, also acceptable to say p < 0.0001.)

d. and e. I will leave these interpretations to you. Remember the mnemonic: if p too low, the null must go.

All of the tests can also be done in TI 83 or 84 Plus calculator. Go to STAT-TESTS-1PropZTest. Enter p0= 0.0224, x= 78, n= 1065, and choose not equal to. Your z test statistic will differ slightly due to rounding, but p-value will not differ to 4 digits.