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Answer:
A) Option C: H0: μ ≥ 7; HA: μ < 7
B) test statistic = -1.75
C) Option C: 0.025 ≤ p-value < 0.05
D) Option C: Do not reject H0 since the p-value is greater than α.
E) Option A: There is insufficient evidence to suggest that Americans sleep less than the recommended 7 hours of sleep.
Step-by-step explanation:
We are given;
Population mean; μ = 7
Sample mean; x = 6.7
Standard deviation; s = 2.1
Sample size; n = 150
A) Defining the hypothesis, we have;
Null Hypothesis; H0: μ ≥ 7
Alternative hypothesis; HA: μ < 7
B) Formula for the test statistic is;
z = (x - μ)/(s/√n)
Plugging in the relevant values, we have;
z = (6.7 - 7)/(2.1/√150)
z = -0.3/0.1715
z = -1.75
C) Using online p-value from z-score calculator attached with; z = - 1.75 ; α = 0.01 and one tailed distribution, we have;
The P-Value = 0.040059
Thus,the most appropriate answer is;
Option C: 0.025 ≤ p-value < 0.05
D) P-value is greater than the significance level, thus we fail to reject the null hypothesis.
E) We will conclude that there is insufficient evidence to suggest that Americans sleep less than the recommended 7 hours of sleep.
