400 students were randomly sampled from a large university, and 289 said they did not get enough sleep. Conduct a hypothesis test to check whether this represents a statistically significant difference from 50%, and use a significance level of 0. 1

The sample proportion represents a statistically significant difference from 50%

Explanation:

The sample proportion is the same as 50%

Alternate hypothesis: The sample proportion is not the same as 50%

z = (p' - p) ÷ sqrt[p(1 - p) ÷ n]

p' is sample proportion = 289/400 = 0.7225

p is population proportion = 50% = 0.5

n is number of students sampled = 400

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

The test is a two-tailed test. Using a 0.01 significance level, critical value is 2.576. The region of no rejection of the null hypothesis is -2.576 and 2.576.

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