Answer:
Hello the options to your question is missing below are the options
A) if sample means were obtained for a long series of samples, approximately 95 percent of all sample means would be between 10 and 16 miles
B.the unknown population mean is definitely between 10 and 16 miles
C.if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians
D.the unknown population mean is between 10 and 16 miles with probability .95
Answer : if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians ( c )
Step-by-step explanation:
95% confidence
interval = 10 to 16 miles
To have 95% confidence signifies that if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians
confidence interval covers a range of samples/values in the interval and the higher the % of the confidence interval the more precise the interval is,
The confidence interval is given by the formula:
m +/- z·(σ/√n)
First, compute the mean:
m = (<span>15.8 + 15.6 + 15.1 + 15.2 + 15.1 + 15.5 + 15.9 + 15.5) / 8
= 15.463
Then, compute the standard deviation:
</span>σ = √[∑(v - m)²/n]
= 0.287
The z-score for a 95% confidence interval is z = 1.96.
Now you can calculate:
m + z·(σ/√n) = 15.463 + 1.96·(0.287/√8)
= 15.463 + 0.199
= 15.662
m - z·(σ/√n) = 15.463 - 1.96·(0.287/√8)
= 15.463 - 0.199
= 15.264
Therefore the confidence interval is (15.264, <span>15.662) and the correct answer is E) none of the above.</span>
