An environmental scientist wants to use a 95% confidence interval to estimate th
ID: 2921912 • Letter: A
Question
An environmental scientist wants to use a 95% confidence interval to estimate the mean number of hours per day her solar panel receives direct sunlight. She observed the panel for 48 randomly selected days and found that the solar panel received an average of 7.1 hours of sunlight per day and the standard deviation was 2.3 hours.
Round your answers to two decimal places.
A. The sampling distribution follows a [ Select ] ["T", "normal", "Chi-square", "F"] distribution.
B. With 95% confidence the population mean number of hours of sunlight the solar panel receives per day for all days is between [ Select ] ["6.1", "2.1", "46", "6.4"] and [ Select ] ["2.5", "8.7", "51", "7.8"] .
C. If many groups of 48 randomly selected days were observed, then a different confidence interval would be produced from each group. About [ Select ] ["5", "1", "95", "99"] percent of these confidence intervals will contain the true population mean number of hours of sunlight per day that the solar panel receives and about [ Select ] ["99", "95", "1", "5"] percent will not contain the true population mean number of hours of sunlight that the solar panel receives.
Explanation / Answer
A)The sampling distribution follows a "T" "distribution.
b) here std error of mean =std deviation/(n)1/2 =0.332
for 95% CI and (n-1=47) degree of freedom t =2.0117
therfore 95% confidence interval =smple mean -/+ t*std error =6.4 to 7.8.
With 95% confidence the population mean number of hours of sunlight the solar panel receives per day for all days is between "6.4" and "7.8"
c)
. If many groups of 48 randomly selected days were observed, then a different confidence interval would be produced from each group. About 95 percent of these confidence intervals will contain the true population mean number of hours of sunlight per day that the solar panel receives and about 5 percent will not contain the true population mean number of hours of sunlight that the solar panel receives