Complete question :
According to one source, 49% of plane crashes are due at least in part to pilot error. Suppose that in a random sample of 100 separate airplane accidents, 61 of them were due to at least in part to pilot error. Complete parts (a) and (b) below. Test the hypothesis that the proportion of airplane accidents due to pilot error is not 0.49. Use a significance level of 0.05.
Determine the null and alternative hypotheses. H0: p Ha: p
Determine the test statistic. Z = (Round to two decimal places as needed.)
Determine the p-value.
Answer:
H0: p = 0.49
Ha: p ≠ 0.49
Zstatistic = 2.45
Pvalue = 0.015
Reject H0, there is sufficient evidence to conclude that population proportion is not 0.49
Step-by-step explanation:
Claim: proportion of airplane accidents due to pilot error is not 0.49
Null and Alternative hypothesis :
H0: p = 0.49
Ha: p ≠ 0.49
Sample size (n) = 100
Number due in part to pilot error = 61
Sample Proportion ph = 61 / 100 = 0.61
Standard Error :
√(p*(1 - p) / n))
√(0.61 * (1 - 0.61) / 100))
√(0. 61 * 0.0039)
= 0.0487749
= 0.049 ( 3 significant figure)
Zstatistic = (ph - p) / SE
Zstatistic = (0.61 - 0.49) / 0.049
Zstatistic = 2.4489795 = 2.45
Using the p value from Z statistic calculator ; α = 0.05, 2 tailed test :
P value = 0.014687 = 0.015
P value < α
0.015 < 0.05
Since the p value is less Than α,
Reject H0, there is sufficient evidence to conclude that population proportion is not 0.49
