400 students were randomly sampled from a large university, and 289 said they did not get enough sleep. Conduct a hypothesis tes

Answer:

The sample proportion shows a statistically significant divergence from 50%

Step-by-step explanation:

Null hypothesis: The sample proportion equals 50%

Alternative hypothesis: The sample proportion does not equal 50%

z = (p' - p) ÷ sqrt[p(1 - p) ÷ n]

p' is the sample proportion = 289/400 = 0.7225

p is the population proportion = 50% = 0.5

n is the number of students surveyed = 400

z = (0.7225 - 0.5) ÷ sqrt[0.5(1 - 0.5) ÷ 400] = 0.2225 ÷ 0.025 = 8.9

The analysis is two-tailed. At a significance level of 0.01, the critical value is 2.576. The acceptance region for the null hypothesis is between -2.576 and 2.576.

Conclusion:

Reject the null hypothesis since the calculated z-score of 8.9 is beyond the bounds established by the critical values of -2.576 and 2.576.

There is compelling evidence to support the assertion that the sample proportion signifies a meaningful difference from 50%.