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
galina1969 [7]
3 years ago
15

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.

Mathematics
1 answer:
Marizza181 [45]3 years ago
8 0

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.

You might be interested in
How do you solve algebraically 8x^2=18
vodka [1.7K]
That would be
x =  + \frac{ \sqrt[]{3} }{ \sqrt[]{2} }
BTW the plus sign is supposed to have this sign underneath it _
Good luck.
5 0
3 years ago
1,023 + _____ = 1,400
denpristay [2]

Answer: 377

1,400 - 1,023 = 377

1,023 + 377 = 1,400

Step-by-step explanation: easy

5 0
2 years ago
Read 2 more answers
A number that multiplies a variable in a term is a _-
Leto [7]
It is called a variable
8 0
3 years ago
Read 2 more answers
A set of three lines that has one point of intersection
Blababa [14]
If the question is, what is it? It is called this figure a pencil of lines.
А pencil of lines can consist of any number of straight, the main thing that they all had one common point. Here you can find a lot of vertical angles and rays.
7 0
3 years ago
Carrington is paid at the same rate each time he baby sits. The graph shows the rate he is paid for different times.
andreyandreev [35.5K]
The answer is D. 4x7+5=33 8x7+5=61. Hope it helps
5 0
3 years ago
Other questions:
  • What is the 9th term of the geometric sequence 4, −20, 100, …?
    10·2 answers
  • (4,?) is on the line y=2x+3. Find the other half of the coordinate
    11·1 answer
  • Round 763,400 to nearest ten thousand explain
    8·1 answer
  • Help me solve this problem please
    8·2 answers
  • PLEASE HELP
    15·1 answer
  • -6+3k-8k+2 simplify the expressions
    11·1 answer
  • 25% of what number equals 10?
    7·1 answer
  • Aniah printed 1-page fliers. She used a printer that can print 1 page every 4.25 seconds. How long did it take her to print 58 f
    13·2 answers
  • Pyramid ABCDE is a square pyramid. What is the lateral area of pyramid ABCDE? 2563√ in² 3843√ in² 5123√ in² 10243√ in² Pyramid A
    12·1 answer
  • WHAT IS THE ANSWER OF A VOLUME OF A CYLINDER WITH A DIAMETER OF 6CM AND HEIGHT OF 12CM
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!