Answer: 0.973
Explanation:
Here are the steps needed to calculate the p-value for a hypothesis test for a proportion:
Determine if the hypothesis test is left tailed, right tailed, or two tailed.
Compute the value of the test statistic.
If the hypothesis test is left tailed, the p-value will be the area under the standard normal curve to the left of the test statistic z0
If the test is right tailed, the p-value will be the area under the standard normal curve to the right of the test statistic z0
If the test is two tailed, the p-value will be the area to the left of −|z0| plus the area to the right of |z0| under the standard normal curve
For this example, the test is a left tailed test.
For this hypothesis test, the proportion of successes is p^=305700≈0.4357.
The test statistic is calculated as follows:
z=p^−p0p0⋅(1−p0)n√
z=0.4357−0.400.40⋅(1−0.40)700√
z≈1.93
The value of the test statistic is 1.93.
Thus the p-value is the area under the Standard Normal curve to the left of a z-score of 1.93.
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.5 0.933 0.934 0.936 0.937 0.938 0.939 0.941 0.942 0.943 0.944
1.6 0.945 0.946 0.947 0.948 0.949 0.951 0.952 0.953 0.954 0.954
1.7 0.955 0.956 0.957 0.958 0.959 0.960 0.961 0.962 0.962 0.963
1.8 0.964 0.965 0.966 0.966 0.967 0.968 0.969 0.969 0.970 0.971
1.9 0.971 0.972 0.973 0.973 0.974 0.974 0.975 0.976 0.976 0.977
2.0 0.977 0.978 0.978 0.979 0.979 0.980 0.980 0.981 0.981 0.982
From a lookup table of the area under the Standard Normal curve, the corresponding area is then 0.973.