1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
melamori03 [73]
3 years ago
12

The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years

for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years.
Required:
a. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites.
b. State the null and alternative hypotheses.
c. Which distribution (normal or Student's t) would you use for this hypothesis test?
d. Calculate the test statistic and p-value.
e. Does it appear that the means are the same? Why or why not?
Mathematics
1 answer:
inn [45]3 years ago
4 0

Answer:

b. The null and alternative hypothesis are:

H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0

c. Student's t distribution, as it is a two-sample test for the difference between means.

d. Test statistic t = 5.42.

P-value = 0

e. They appear to be significantly different, as the sample data gives strong evidence that the difference is greater than 0.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that the mean life spans in the county is significantly different for whites and nonwhites.

Then, the null and alternative hypothesis are:

H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0

The significance level is 0.05.

The sample 1 (white), of size n1=124 has a mean of 45.3 and a standard deviation of 12.7.

The sample 2 (non-white), of size n2=82 has a mean of 34.1 and a standard deviation of 15.6.

The difference between sample means is Md=11.2.

M_d=M_1-M_2=45.3-34.1=11.2

The estimated standard error of the difference between means is computed using the formula:

s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12.7^2}{124}+\dfrac{15.6^2}{82}}\\\\\\s_{M_d}=\sqrt{1.301+2.968}=\sqrt{4.269}=2.066

Then, we can calculate the t-statistic as:

t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{11.2-0}{2.066}=\dfrac{11.2}{2.066}=5.42

The degrees of freedom for this test are:

df=n_1+n_2-2=124+82-2=204

This test is a two-tailed test, with 204 degrees of freedom and t=5.42, so the P-value for this test is calculated as (using a t-table):

\text{P-value}=2\cdot P(t>5.42)=0.0000002

As the P-value (0.0000002) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the mean life spans in the county is significantly different for whites and nonwhites.

You might be interested in
Find each product.<br><br> (X3+2x2)x4<br><br> PLEASE HELP!!! ASAP!!!
Rina8888 [55]

Answer:

4x^3+8x^2

Step-by-step explanation:

Multiply each term:

4x^3+8x^2

PLZ MARK ME BRAINLIEST

4 0
3 years ago
Jane sells 8 times as many Volvos as Melissa. If the difference in their sales is 35, how many cars did Jane sell?
Usimov [2.4K]
Here we have 2 variables we need to calculate:
x - how many Volvos Jane sold
y - how many Volvos Melissa sold

We write system of equations:
x = 8*y
x - y = 35
------------
8y - y = 35
7y = 35
y = 5
x = 8*5 = 40

Jane sold 40 cars.
8 0
3 years ago
Mae Ling earns a weekly salary of 325$ plus a 6.5% commission on sales at a gift shop. how much would she make in a work eek if
REY [17]
6.5% of 4,800= 312
325+312= 637
$637
5 0
3 years ago
Read 2 more answers
Richard buys one tooth cleaning kit for $25 and a toothbrush for $15. He spends the rest of his money on body soap. He has $80 a
wariber [46]
He can buy up to 8 bodies of soap.
I hope this helps!
8 0
3 years ago
Read 2 more answers
The ninth graders are hosting the next school dance. They would like to make at least a $500 profit from selling tickets. The ni
kykrilka [37]

Answer:

They would earn 900 dollars at the door

5 0
3 years ago
Other questions:
  • Find m A. 20<br> B. 40<br> C. 60<br> D.120
    8·2 answers
  • What is the volume of the container needed to store 0.8 moles of argon gas at 5.3 atm and 227°C?. . (Given: R = 0.08205 l · atm/
    9·2 answers
  • In a class, 12 out of 25 students are female. what percent of students are female?
    9·1 answer
  • Mr. Walker was hiking across Massachusetts. He has three days to cover 70 miles. On the first day, he walked 6 hours at a speed
    7·2 answers
  • Product of -3x(5x 1)
    15·1 answer
  • Pine trees and juniper trees are common to the San Bernardino
    9·1 answer
  • Match them BRAINLIEST IF CORRECT ​
    9·1 answer
  • Convert radical to exponential<br> 6√(10x)^7<br> ∛43<br> √(5x)^5
    8·1 answer
  • Investment account starting balance of $7400 in one year it had increased by 7.5%. How much is this in dollars
    5·1 answer
  • Answer questions (1-4) Please help…
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!