Question
In: Statistics and Probability
Student's t Distribution CI The manager of The Cheesecake Factory in Boston would like to know...
Student's t Distribution CI
The manager of The Cheesecake Factory in Boston would like to know the mean number of customers served on weekdays. She believes that the number of customers served follows a Normal distribution. She reports that on six randomly selected weekdays an average of 158.3 customers were served with a sample standard deviation of 52.2.
a. Calculate the standard error of the sample mean.
b Find the t-critical value for a 99% confidence interval with a sample size of 6.
c. Calculate a 99% confidence interval of the mean.
d. Interpret the confidence interval in the context of the problem.
Solutions
Expert Solution
Solution :
Given that,
Point estimate = sample mean = 
= 158.3
sample standard deviation = s = 52.2
sample size = n = 6
Degrees of freedom = df = n - 1 = 6 - 1 = 5
a) SE = (s /
b) At 99% confidence level
= 1 - 99%
=1 - 0.99 =0.01
/2
= 0.005
t/2,df
= t0.005,5 = 4.032
c) Margin of error = E = t
/2,df
* SE
= 4.032 * 21.31
Margin of error = E = 85.92
The 99% confidence interval estimate of the population mean is,
±
E
= 158.3 ± 85.92
= ( 72.38, 244.22 )
d) We are 99% confident that the true mean of customers served on weekdaysbetween 72.38 and 244.22.
orchestra answered 2 years agoRelated Solutions
The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the...
The manager of The Cheesecake Factory in Boston reports that on
six randomly selected weekdays, the number of customers served was
120, 130, 100, 205, 185, and 220. She believes that the number of
customers served on weekdays follows a normal distribution.
Construct the lower bound of the 90% confidence interval for the
average number of customers served on weekdays. (Round the sample
standard deviation to 2 decimal places, the "t" value to 3 decimal
places, and the final answer...
The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate...
The Student's t distribution table gives critical values for the
Student's t distribution. Use an appropriate d.f. as the row
header. For a right-tailed test, the column header is the value of
α found in the one-tail area row. For a left-tailed test, the
column header is the value of α found in the one-tail area row, but
you must change the sign of the critical value t to −t. For a
two-tailed test, the column header is the value...
13) The Student's t distribution table gives critical values for the Student's t distribution. Use an...
13)
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the...
The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate...
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the value...
12) The Student's t distribution table gives critical values for the Student's t distribution. Use an...
12)
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the...
The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate...
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
αfound in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the value of...
The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate...
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the value...
The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate...
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the value...
The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate...
The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the value...
What happens to a Student's t-distribution as the degrees of freedom increase? a.A student's t-distribution diverges...
What happens to a Student's t-distribution as the degrees of
freedom increase?
a.A student's t-distribution diverges from the standard normal
distribution as the degrees of freedom increases
b.A student's t-distribution converges to the standard normal
distribution as the degrees of freedom increases
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- I would like to integrate a bubble sort into this binary search in c ++ Thank...
- Answer the bottom in 1-2 paragraphs Classical conditioning is a learned behavior where previously neutral response...
- identify one intrapersonal relationship and evaluate its component.
- Using Python in vs code: The distribution of letters in a document has a distinctive and...
- Why is De Beers exploring the diamond reselling market? How does the creation of IIDV affect...
- programming in Python The body mass index (BMI) is calculated as a person’s weight (in lb)...
- 1. Show the steps in merging A and B into C where A= 8, 12, 19,...
ADVERTISEMENT