Answer:
a) Standard Error = 0.6578
b) 99% confidence interval = (7.303, 10.697)
c) A population mean of 8.5 hours would not surprise the psychologist as this is within the confidence interval.
Step-by-step explanation:
a) Standard error = Standard deviation/√n
n = sample size = 250
Standard deviation = 10.4
Standard error = (10.4/√250)
Standard error = 0.6578
b) 99% confidence interval
Confidence interval = (Sample mean) ± (Margin of error)
Sample mean = 9 hours
Margin of Error = (critical value) × (standard error or standard deviation of the distribution of sample means)
Critical value for a 99% confidence interval = 2.58 (from the z-tables)
Standard error or standard deviation of the distribution of sample means = 0.6578
margin of error = 2.58 × 0.6578 = 1.697
Confidence interval = 9 ± 1.697
Lower limit of the confidence interval = 9 - 1.697 = 7.303 hours
Upper limit of the confidence interval = 9 + 1.697 = 10.697 hours
99% confidence interval = (7.303, 10.697)
c) A population mean of 8.5 hours would not surprise the psychologist as this is within the confidence interval.
Hope this Helps!!!
