According to the Centers for Disease Control and Prevention (February 18, 2016), 1 in 3 American adults don’t get enough sleep. A researcher wants to determine if Americans are sleeping less than the recommended 7 hours of sleep on weekdays. He takes a random sample of 150 Americans and computes the average sleep time of 6.7 hours on weekdays. Assume that the population is normally distributed with a known standard deviation of 2.1 hours. Test the researcher’s claim at α = 0.01
a. Select the relevant null and the alternative hypotheses.
A. H0: μ = 7; HA: μ ≠ 7
B. H0: μ ≤ 7; HA: μ ≥ 7
C. H0: μ ≥ 7; HA: μ < 7
b. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
Test statistic = ?
c. Find the p-value
A. p-value < 0.01
B. 0.01 ≤ p-value < 0.025
C. 0.025 ≤ p-value < 0.05
D. 0.05 ≤ p-value < 0.10
E. p-value ≥ 0.10
d. What is the conclusion at α = 0.01?
A. Reject H0 since the p-value is greater than α.
B. Reject H0 since the p-value is smaller than α.
C. Do not reject H0 since the p-value is greater than α.
D. Do not reject H0 since the p-value is smaller than α.
e. Make an inference.
A. There is insufficient evidence to suggest that Americans sleep less than the recommended 7 hours of sleep.
B. There is sufficient evidence to suggest that Americans sleep less than the recommended 7 hours of sleep.
Answers
Answer:
A) Option C: H0: μ ≥ 7; HA: μ < 7
B) test statistic = -1.75
C) Option C: 0.025 ≤ p-value < 0.05
D) Option C: Do not reject H0 since the p-value is greater than α.
E) Option A: There is insufficient evidence to suggest that Americans sleep less than the recommended 7 hours of sleep.
Step-by-step explanation:
We are given;
Population mean; μ = 7
Sample mean; x = 6.7
Standard deviation; s = 2.1
Sample size; n = 150
A) Defining the hypothesis, we have;
Null Hypothesis; H0: μ ≥ 7
Alternative hypothesis; HA: μ < 7
B) Formula for the test statistic is;
z = (x - μ)/(s/√n)
Plugging in the relevant values, we have;
z = (6.7 - 7)/(2.1/√150)
z = -0.3/0.1715
z = -1.75
C) Using online p-value from z-score calculator attached with; z = - 1.75 ; α = 0.01 and one tailed distribution, we have;
The P-Value = 0.040059
Thus,the most appropriate answer is;
Option C: 0.025 ≤ p-value < 0.05
D) P-value is greater than the significance level, thus we fail to reject the null hypothesis.
E) We will conclude that there is insufficient evidence to suggest that Americans sleep less than the recommended 7 hours of sleep.
Related Questions
Five computer program modules are ranked as M1, M2, M3, M4, and M5 according to the ascending order of effort required to debug them, among which M1 requires the least amount of effort and M5 requires the most amount of effort. A software engineer must randomly select three program modules from the five modules. He (or she) does not know the amount of effort each module costs when selecting.
A) What is the sample space?
B) Let A be the event that one selected module requires the least amount of effort. List the outcomes in A, and calculate the probability of A.
C) Let B be the event that the one selected module requires the most effort. List the outcomes in B, and calculate the probability of B.
D) List the outcomes in the compound event AnB, and calculate the probability of it.
E) List the outcomes in the compound event AUB, and calculate the probability of it.
F) List the outcomes in the compound event AnB, and calculate the probability of it.
G) List the outcomes in the compound event AUB, and calculate the probability of it.
H) Are events A and B mutually exclusive? Explain why?
Answers
Answer:
Follows are the solution to this question:
Step-by-step explanation:
Technician selects three out of 5 systems
In C(5,3)=10ways, this can be achieved
In part a:
Space sample chooses 3 of a 5 systems
[tex](M_1, \ M_2,\ M_3),[/tex][tex](M_1,M_2,M_4) \ (M_1,M_2,M_5) \ (M_1,M_3,M_4) \ (M_1,M_3,M_5),[/tex][tex](M_1,M_4,M_5) \ (M_2,M_3,M_4)\ (M_2,M_3,M_5) \ (M_2,M_4,M_5),(M_3,M_4,M_5)}[/tex]
In point b:
A =MODULE WHICH INCLUDE M1 minimal amount of effort
Outcomes probable =
[tex](M_1,M_2,M_3),\ (M_1,M_2,M_4) \ (M_1,M_2,M_5)\ (M_1,M_3,M_4)\\\\(M_1,M_3,M_5),\ (M_1,M_4,M)5)\ =\ 6[/tex]
[tex]\to p(A)=\frac{6}{10}\\\\[/tex]
[tex]=0.6[/tex]
In point c:
B = highest effort that is [tex]M_5[/tex]
Potential result=
[tex](M_1,M_2,M_5) \ (M_1,M_3,M_5) \ (M_2,M_3,M_5)\(M_2,M_4,M_5) \\ (M_2,M_4,M_5), \ (M_3,M_4,M_5) \ =\ 6 \\\\[/tex]
[tex]\to B= \frac{6}{10} \\\\[/tex]
[tex]=0.6[/tex]
[tex]\to P(B)=10[/tex]
In point d:
[tex]\to \ A \ intersection \ B=(M_1,M_2,M_5), \ (M_1,M_3,M_5) \ ,(M_1,M_4,M_5)[/tex]
[tex]\to A (A \ intersection \ B) = \frac{3}{10} \\\\\ \ \ \ \ \[/tex]
[tex]=0.3[/tex]
In point e:
[tex]\to (A \cup B) = (M_1,M_2,M_3),\ (M_1,M_2,M_4)\ (M_1,M_2,M_5)(M_1,M_3,M_4)\ (M_1,M_3,M_5), \\ (M_1,M_4,M_5)\ (M_2,M_3,M_5) \ (M_2,M_4,M_5),(M_3,M_4,M_5) \ = \ 9[/tex][tex]\to P(A \cap B)=\frac{9}{10}[/tex]
[tex]= 0.9[/tex]
In point f:
[tex]\to (A\cap B) = \frac{3}{10}[/tex]
[tex]= 0.3[/tex]
In point g:
[tex]\to (A \cup B) = \frac{7}{10}[/tex]
[tex]=0.7[/tex]
In point h:
[tex]\to p(A \cap B) = 0.3 \neq 0[/tex]
What is 20.305 in expanded form
Answers
Answer:
5,000 + 300 + 20 + 5 = 5,325
Step-by-step explanation:
Why can you use cross products to solve the proportion StartFraction 18 over 5 EndFraction = StartFraction x over 100 EndFraction for x?
A)because 18 times 100 is equal to 5 times x, which means that x is equal to 36
B)because 18 times 100 is equal to 5 times x, which means that x is equal to 360
C)because 18 times x is equal to 5 times 100, which means that x is equal to 36
D)because 18 times x is equal to 5 times 100, which means that x is equal to 360
Answers
Answer:
Because 18 times 100 is equal to 5 times x, which means that x is equal to 360
Step-by-step explanation:
18/5=x/100
Cross product
18*100=5*x
1800=5x
x=1800/5
x=360
because 18 times 100 is equal to 5 times x, which means that x is equal to 360
18 times 100 is equal to 5 times x, which means that x is equal to 360
Step-by-step explanation:
4x⁴• 3x⁸
_______
6x⁵
Answers
Answer:
2x^7
can you also please mark me as brainliest?
Math Questions. 5+ points
Answers
3. Solve the equation
| 3x - 1| + 5 = 3
Answers
Answer:
Its not possible
Step-by-step explanation:
a absolute value equation cant equal a negative number
The quantity 32 minus 16 multiplied by 9
Answers
The value of the statement the quantity 32 minus 16 multiplied by 9 is
- 112.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The given statement is the quantity 32 minus 16 multiplied by 9.
The numerical form of the statement is,
= (32 - 16×9).
First, we'll multiply according to PEMDAS rule.
= (32 - 144).
= - 112.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ2
The value of the statement the quantity 32 minus 16 multiplied by 9 is
- 112.
We have,
A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The given statement is the quantity 32 minus 16 multiplied by 9.
The numerical form of the statement is,
= (32 - 16×9).
First, we'll multiply according to PEMDAS rule.
= (32 - 144).
= - 112.
learn more about numerical expressions here :
brainly.com/question/29199574
#SPJ6
Help me with this question please
Answers
Answer:
1 blank. 24
2 blank. 42
3 blank. 56
Step-by-step explanation:
This question is a matter of ratios
The ratio being 7:6
7= # of hamburgers
6= # of hotdogs
To find each answer, you have to set the ratios equal to each other
7/6=28/?
7 times what equals 28
7 times 4 equals 28, so then you multiply 4 by 6 to get you number of hotdogs in that equation
You'll repeat the process for all the other equations as well
Which statement correctly compares the function shown on this graph with the function y =5x+5.
Answers
Answer: D
Step-by-step explanation:
The function shown on the graph has the same rate of change but lower starting point
the answer is D!
the function shown on the graph has the same rate of change but a lower starting point.
A large glass marble made in West Virginia has a diameter of 2 cross times 10 to the power of minus 2 end exponent meters. The state of West Virginia is about 4 cross times 10 to the power of 5 meters in length. Which number is closest to how many large glass marbles it would take to measure the length of West Virginia?
Answers
Answer:
20000000 large glass marbles
Step-by-step explanation:
Given
[tex]Diameter = 2 * 10^{-2}m[/tex] --- Marble
[tex]Length = 4 * 10^5m[/tex] --- Virginia
Required
Determine the number or marbles that measures the length of Virginia
This is calculated as thus:
[tex]Number = \frac{Length}{Diameter}[/tex]
[tex]Number = \frac{4 * 10^{5}m}{2 * 10^{-2}m}[/tex]
[tex]Number = \frac{4 * 10^{5}}{2 * 10^{-2}}[/tex]
[tex]Number = \frac{2 * 10^{5}}{10^{-2}}[/tex]
Apply Law of Indices
[tex]Number = 2 * 10^{5 - (-2)}[/tex]
[tex]Number = 2 * 10^{5 +2}[/tex]
[tex]Number = 2 * 10^7[/tex]
[tex]Number = 2 * 10000000[/tex]
[tex]Number = 20000000[/tex]
How can You use mental math for 878 + 534=
Answers
in my head i would say 8+4=12 carry the 1 so 7+3+1= 11 carry the 1 then 8+5+ 1= 14 so the answer would be 1,412
Answer:
the answer would be 1412
Step-by-step explanation: Take the '4' in 534, add it to the 878 in your head. Thus resulting in 882. Then add the 30 to this number. After adding 30, you should get 912. Then add 500, and your answer is 1412.
Is (0,3) a solution of the equation x + y = 3
Answers
(look at image) gggggggggggg
Answers
Answer:
hard to see a little
Step-by-step explanation:
Somebody help me with my math work please
Answers
Answer:
OK what do you need help with
What is the value of 5/6 divided by 3/4
Answers
Answer:
the answer is 1 & 1/9! hope that helps! :D
Answer:10/9
Step-by-step explanation:
An item costs $ 340 before tax, and the sales tax is $ 13.60 . what is the sales tax rate
Answers
yeahStep-by-step explanation:
Answer:
4%
Step-by-step explanation:
To find the sales tax rate you need to divide the tax amount by the item amount so in this case it is 13.60/340 with an answer of 0.04 meaning the tax rate is 4%. Hope this helps!
A cafeteria makes 2,516 pounds of white rice and 608 pounds of brown rice every month. After 6 months, how many pounds of rice does the cafeteria make?
Answers
Answer:
18744 lbs
Step-by-step explanation:
2516+608= 3124
multiply by the 6 months
3124*6=18744
a total of 18744 lbs.
Answer:
18,744 pounds of rice
Step-by-step explanation:
2,516 pounds of white rice + 608 pounds of brown rice = 3,124 pounds of rice each month.
3,124 x 6 months = 18,744 pounds of rice
Kerrie is tiling the floor of a kitchen. The kitchen floor measures 11.3 feet by 9.25 feet. She orders enough tile for 99 square feet. Which statement about the amount of tiles is correct.
sorry dont have time to type the answers but if you got this question and know the answer just tell me!
Answers
Answer:
AAAAAAAAAA
Step-by-step explanation:
Joey made this
graph to show how many incorrect
answers students got on a test. how
many students got 3 answers incorrect?
how do you know?
number of students
Answers
Find the lowest common multiple of 35 and 55
Answers
Answer: The lowest common multiple between 35 and 55 is 385.
Mark and Robyn used base-ten blocks to show that 200 is 100 times as much as 2
Ex
Whose model makes sense? Whose model is nonsense? Complete the explanation.
Step
Mark's Work
Robyn's Work
М.
th
Te
200
200
Mark's
model does not make sense. That person's model shows 20 instead of 200
That person's model shows that 200
is 10 times as much as
model makes sense. That person's model shows that 200 is
times as
much as 2
Answers
Answer:
See Explanations
Step-by-step explanation:
The steps in the question isn't clear enough, however the question is answerable.
From the question, we understand that one model shows that:
200 is 10 times 20
While the second model shows that
200 is 10 times 2
The first model that says
200 = 10 times 20 makes sense.
This is so, because 200 = 20 * 100
While the other model which says
200 = 10 * 2 is nonsense.
This is so because, 200 ≠ 10 * 2
16 inches to 2 feet. Translate the ratio into a fraction in simplest form
Answers
Answer:
2/3
Step-by-step explanation:
there are 12in in a foot so
16/24
simplify
8/12
2/3
HELP ME ASAP PLSSSSSSSS
Answers
Answer:
The answer is B.50
Step-by-step explanation
Replace x with 50
(50+20)=70+50 from the other lone xFind z by subtracting 180 by the external angle (150) and get 30Add to get 180 which is what a triangle adds up toHELP WILL GIVE BRAINLIEST AND 100+ POINTS
what is the equation in slope intercept form of the lienar function represented by the table
Answers
Answer:
it is Y=Mx+B
Step-by-step explanation:
m=slope
b=intercept
x/s= -10
the first one is a fraction
Answers
Answer:
x=-10s. s=-x/10
Step-by-step explanation:
what could equal 16 if your x4
Answers
Answer:
i think u are saying this
Answer:if you’re saying what multiplied by 4 equals 16 is 4.
Step-by-step explanation:
Can someone help me with this problem pleaseee
Answers
Answer:
22.11 percent
A sum of Rs. 1800 borrowed for 2 years at the rate of 12 % per annum. Find
the interest?
Answers
Answer:
72
Step-by-step explanation:
principal (P)=1800
time(T)=2yrs
rate(R)=2%
SI=?
now,
SI=PTR÷100
= 1800×2×2÷100
=7200÷100
=72
so interest is 72.
hope this will help you :D
Please help!!!!!! I will make you brainly!!!!!!!!!!!!
Answers
Answer:
The last option
Step-by-step explanation:
Trust me, I know it is correct
What do you need to do to rationalize a denominator with a cube root in it?
Answers
Answer:
When a denominator has a higher root, multiplying by the radicand will not remove the root. Instead, to rationalize the denominator we multiply by a number that will yield a new term that can come out of the root. For example, with a cube root multiply by a number that will give a cubic number such as 8, 27, or 64.