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Answer:
A) Null hypothesis;H0: μ ≥ 7
Alternative Hypothesis;Ha: μ < 7
B) t ≈ -1.75
C) 0.025 ≤ p-value < 0.05
D) Do not reject H0 since the p-value is greater than α
E) 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
Sample Standard deviation; s = 2.1
Level of significance; α = 0.01
Sample size; n = 150
A) Now, the hypotheses can be stated as;
Null hypothesis;H0: μ ≥ 7
Alternative Hypothesis;Ha: μ < 7
B) The test statistic will be calculated from the formula;
t = (x' - μ)/(s/√n)
Plugging in the relevant values, we have;
t = (6.7 - 7)/(2.1/√150)
t = -0.3/0.1715
t = -1.7493
t ≈ -1.75
C) From online p-value from t-score calculator attached using t-score of -1.75; DF = 150 - 1 = 149; significance level of 0.01 and one tail, we have;
The p-value = 0.041088
The closest answer among the options is;
0.025 ≤ p-value < 0.05
D) Since the p-value is greater than the significance level of 0.01, thus we will fail to reject the null hypothesis
E) From D above, we will conclude that there is insufficient evidence to suggest that Americans sleep less than the recommended 7 hours of sleep.
