Construct a 99% confidthence interval for the population mean .Assume the population has a normal distribution. A group of 19 randomly selected employees has a mean age of 22.4 years with a standard deviation of 3.8 years. Round to the nearest tenth.A] Determine the critical value ta/2 with n-the 1 degrees of freedomB] Determine the lower and upper bound of the confidence intervalC] Interpret the confidence interval.

Question
Asked Apr 23, 2019

Construct a 99% confidthence interval for the population mean .Assume the population has a normal distribution. A group of 19 randomly selected employees has a mean age of 22.4 years with a standard deviation of 3.8 years. Round to the nearest tenth.

A] Determine the critical value ta/2 with n-the 1 degrees of freedom

B] Determine the lower and upper bound of the confidence interval

C] Interpret the confidence interval.

check_circle

Expert Answer

star
star
star
star
star
1 Rating
Step 1

Solution:

Part (a): Finding the critical value tα/2 with n-1 degrees of freedom:

Given that, the sample size n =19 and sample mean, x-bar =22.4 with its corresponding sample standard deviation, s = 3.8.

Here the confidence interval is 99%.

Therefore, α = 0.01.

The degrees of freedom, n - 1 = 19 - 1 = 18,

Step 2

From the EXCEL, using the formula, =T.INV.2T (0.01,18), the critical value is 2.878.

Therefore, the critical value tα/2 with 18 degrees of freedom is 2.878.

Step 3

Part (b): Finding the upper and lower bound of the confidence interval:

The population standard deviation is unknown here. Therefore, z-test cannot be used here. In this situation student’s t-distribution can be used. As the sample size is large it can be used th...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Hypothesis Testing

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: For T-tests on related measures, my number of subjects is odd. How do I calculate the differential i...

A: In such cases, you can turn to  Repeated measures ANOVA which can detect differences in mean scores ...

question_answer

Q: Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) sho...

A: given x represent the dollar amount spent on supermarket impulse buying in a 10-minute shopping inte...

question_answer

Q: A statistical program is recommended. Electromagnetic technologies offer effective nondestructive se...

A: Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any ...

question_answer

Q: A manufacturer of a certain type of hardware has two manufacturing facilities and wants to compare t...

A: Conditions:The conditions for the two proportion test for sample sizes n1 and n2 with sample proport...

question_answer

Q: Part G-I, explain TI84 USE IF APPLICABLE

A: g) Computation of F-statistic:F-statistic can be obtained by dividing the mean square of model by th...

question_answer

Q: Which statement regarding correlation is true? A. The dependent variable is assigned to the Y axi...

A: Correlation coefficient - r:The Karl Pearson’s product-moment correlation coefficient or simply, the...

question_answer

Q: You want to obtain a sample to estimate a population proportion. Based on previous evidence, you bel...

A: According to previous evidence, the population proportion (p) is 36%, that is, 0.36.Here, the margin...

question_answer

Q: You receive a brochure from a large university. The brochure indicates that the mean class size for​...

A: According to the given question, to test the claim that The brochure indicates that the mean class s...

question_answer

Q: In a survey of 4061 ​adults, 738 say they have seen a ghost. Construct a​ 99% confidence interval fo...

A: In this question, it has been given that 738 people out of 4061 people have seen the ghost, we have ...