Question

a)

A sample of 256 items is taken from an assembly line which produces 10000 items per day. It is found
that 16 of the sampled items are defective. A wholesale company won't buy the product from this assembly line if the defective rate is more than 0.05. If you were to conduct a hypothesis test your hypotheses would be

Group of answer choices

H0:x¯=0.5Ha:x¯>0.05

H0:p=0.05Ha:p>0.05

H0:μ=0.05Ha:μ>0.05

H0:p^=0.0625Ha:p>0.05

b)

A sample of 256 items is taken from an assembly line which produces 10000 items per day. It is found
that 16 of the sampled items are defective. An approximate 95% confidence interval for the proportion of
defectives produced that day is

Group of answer choices

0.0625 ± .03

0.0256 ± 0.0031

0.0256 ± 0.0016

0.0625 ± .0151

0.00016 ± 0.0003

Answer 1

(a)

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.05

H_a : p > 0.05

(b)

Point estimate = sample proportion = = x / n = 16 / 256 = 0.0625

Z_/2 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.0625 * 0.9375) / 256)

= 0.03

0.0625   0.03