Hawaiians are known to have an active lifestyle, enjoying the fresh air and natural beauty the islands have to offer. The life expectancy of the US population across all 50 states is µ=78.62 years with a standard deviation σ=16.51 years. A randomly selected sample of 100 Hawaiians show an average life expectancy x̅=82.52 years. Is Hawaiians’ average life expectancy significantly different from 78.62, assuming α=0.01?

Question
Asked Oct 4, 2019
1 views

Hawaiians are known to have an active lifestyle, enjoying the fresh air and natural beauty the islands have to offer. The life expectancy of the US population across all 50 states is µ=78.62 years with a standard deviation σ=16.51 years. A randomly selected sample of 100 Hawaiians show an average life expectancy x̅=82.52 years. Is Hawaiians’ average life expectancy significantly different from 78.62, assuming α=0.01?

check_circle

Expert Answer

Step 1

State the appropriate hypothesis:

Denote the population mean life expectancy of the US population across all 50 states as μ and is 78.62 years. The standard deviation is 16.51. The sample size is 100 and the sample average life expectancy is 85.52 years.

The claim is whether or not the Hawaiians average life expectancy to be changed from 78.62.

The hypotheses are given below:

Null hypothesis:

H0 : μ = 78.62

That is, the Hawaiians average life expectancy is equal to 78.62 years.

Alternative hypothesis:

H1 : μ ≠ 78.62 (Two tail test).

That is, the Hawaiians average life expectancy is not equal to 78.62 years.

Step 2

Obtain the test statistic value.

Here, the population standard deviation is known.

Under null hypothesis the population mean life expectancy of the US population across all 50 states is μ0 = 78.62.

The sample average life expectancy is x-bar = 85.52, the sample size is n = 100.

Test statistic:

The test statistic for hypothesis test for mean is given by:

Z =
Tsample mean, 4 hypothesized mean
a population standard deviaton, n
-
sample size
=
The test statistic value is obtained as 4.18 from the calculation given below
85.52 78.62
16.512
100
6.9
=
1.651
= 4.18
help_outline

Image Transcriptionclose

Z = Tsample mean, 4 hypothesized mean a population standard deviaton, n - sample size = The test statistic value is obtained as 4.18 from the calculation given below 85.52 78.62 16.512 100 6.9 = 1.651 = 4.18

fullscreen
Step 3

Obtain the critical value:

The level of significance is α = 0.01.

The critical value is obtai...

a 0.01
0.005
2
Excel formula
Z00052NORM.S.INV(0.99)
help_outline

Image Transcriptionclose

a 0.01 0.005 2 Excel formula Z00052NORM.S.INV(0.99)

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

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Draw a vertical line through a normal distribution for each of the following z-score locations. Dete...

A: 1(a) The provided z value is 1.00 for which the graph is shown below,

question_answer

Q: If there are 57 cards in a deck and 12 are dealt to each student, how many 12 card possibilities are...

A: Combination Rule:The arrangement of r objects from n different objects is given by:

question_answer

Q: Use the data in the following​ table, which lists​ drive-thru order accuracy at popular fast food ch...

A: From the given information, the table is,  ABCDTotalOrder Accurate318261232127938Order not accurate3...

question_answer

Q: We wish to estimate the mean pre-pregnancy weight of women using a 95% CI. We have a sample of 100 w...

A: Alpha = 1 - Confidence Interval               = 1 - 95%               = 1-0.95              =0.05Mar...

question_answer

Q: 23. Composite Drug Test Based on the data in Table 4-1 on page 146, assume that the probability of a...

A: Obtain the probability that randomly selected person testing negative for drug use:It is given that ...

question_answer

Q: Hector is out on an archeological dig. He randomly selected 563 artifacts that he encountered at a p...

A: Given Datan = no of artifacts encountered at a particular site = 563x = no of pottery shards = 271sa...

question_answer

Q: Calculate the compound amount. Use the compound amount formula and a calculator. P=$9100, r=5% compo...

A: From the given information, P=$9,100, r=5%, n=12 and t=3 years.

question_answer

Q: Dr. Samwell Tarly wants to estimate the number of books checked out of the library in the past year....

A: It is given that the mean is 10,000 and the standard deviation is 10.

question_answer

Q: Forty-eight percent of all Californians registered voters prefer life in prison without parole over ...

A: It is given that P(C) is 0.48, P(C|L) is 0.55 and P(L) is 0.376.