Answer:
Step-by-step explanation:
Null hypothesis: National proportion P ≥ sample proportion
Alternative hypothesis: National proportion P < sample proportion
Collect the Data.
Sample size n = 348, population proportion P = 0.41,
a. What is the sample proportion? Use 4 decimal places.
Sample proportion p = 132/348 = 0.3793
b. What is the standard deviation for this problem?
The standard deviation can be calculated using this formula:
√[(p x (1-p)) / n] = √[(0.3793 x (1 - 0.3793) / 348
= √[(0.3793 x 0.6203) / 348]
= √(0.2354 / 348)
= √0.0006765
SD = 0.026
c. The conditions are met:
The sampling method is simple random sampling: Yes
Each sample point can result in just two possible outcomes: a success; have engaged in binge drinking and a failure: have not engaged in binge drinking
The sample includes at least 216 failures and 132 successes
The population size is at least 20 times as big as the sample size: college students nationwide are even 20 times more than 348.
d) What is the test statistic?
z = (p - P) / σ
z = (0.3793 - 0.41) / 0.026
z = (-0.0307 / 0.026)
z = -1.18
At a 5% level of significance, where α= 0.05, p value for -1.18 for a one tailed test using the p value calculator is 0.119, the result is not significant at p < .05 thus, concluding that we fail to reject the null as there is not enough evidence to conclude students enrolled at this college that binge drink is lower than the national proportion of students that binge drink
