A manufacturer claimed that at least 95% of the equipment which he supplied to a factory conformed to specifications. An examinations of a sample of 200pieces of equipment revealed that 18 were faulty. Test this claim at 5% level of significance.
Null Hypothesis (H0): The proportion of faulty equipment is greater than or equal to 5% (p >= 0.05)
Alternate Hypothesis (H1): The proportion of faulty equipment is less than 5% (p < 0.05)
First, calculate the sample proportion of faulty equipment:
p̂ = 18/200 = 0.09
Next, calculate the standard error:
SE = sqrt((0.05 * 0.95) / 200) = 0.0212
Then, calculate the z-score:
z = (0.09 - 0.05) / 0.0212 = 1.8868
At a 5% level of significance, the critical z-value is -1.645 (one-tailed test).
Since the calculated z-value (1.8868) is greater than the critical z-value (1.645), we reject the null hypothesis.
Therefore, there is enough evidence to conclude that the proportion of faulty equipment is less than 5% and thus, the manufacturer's claim is incorrect.