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
Tamiku [17]
3 years ago
11

Suppose the coffee industry claimed that the average U.S. adult drinks 1.7 cups of coffee per day. To test this claim, a random

sample of 34 adults was selected, and their average coffee consumption was found to be 1.95 cups per day. Assume the standard deviation of daily coffee consumption per day is 0.5 cups. Using a = 0.10, answer the following questions:
a. Is the coffee industryâs claim supported by this sample?
b. Determine the p-value for this test.
c. Verify your results using PHStat.
Mathematics
1 answer:
kvv77 [185]3 years ago
5 0

Answer:

a) This t-value obtained (2.92) is in the rejection region (t > 1.69), hence, the sample does not support the cofdee industry's claim.

b) p-value for this test = 0.006266

c) The p-value obtained for this test is lesser than the significance level at which the test was performed, hence, we can reject the nuĺl hypothesis and say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.

Step-by-step explanation:

a) Degree of freedom = n - 1 = 34 - 1 = 33

The critical value of t for a significance level of 0.10 and degree of freedom of 33 = 1.69

Since we are testing in both directions whether the the average U.S. adult drinks 1.7 cups of coffee per day using our sample,

The rejection region is t < -1.69 and t > 1.69

So, we compute the t-statistic for this sample data to test the claim.

t = (x - μ)/σₓ

x = sample mean = 1.95 cups of coffee per day

μ₀ = The standard we are comparing against = 1.7 cups of coffee per day

σₓ = standard error = (σ/√n)

σ = standard deviation = 0.5 cups

n = Sample size = 34

σₓ = (0.5/√34) = 0.0857492926 = 0.08575

t = (1.95 - 1.70) ÷ 0.08575

t = 2.9154759464 = 2.92

This t-value obtained is in the rejection region, hence, the sample does not support the cofdee industry's claim.

b) Checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 34 - 1 = 33

Significance level = 0.10

The hypothesis test uses a two-tailed condition because we're testing in both directions.

p-value (for t = 2.92, at 0.10 significance level, df = 33, with a two tailed condition) = 0.006266

c) To use PHStat, the claim that the average U.S. adult drinks 1.7 cups of coffee per day is the null hypothesis.

The alternative hypothesis is that the real number of cups of coffee that the average U.S. adult drinks as obtained from the sample data, is significantly different from the 1.7 in the coffee industry's claim.

The p-value obtained from PHstat = 0.0063

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.10

p-value = 0.0063

0.0063 < 0.10

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.

Hope this Helps!!!

You might be interested in
Which of the following is an x-intercept of the function, f(x) = x3 – x2 - 8x +12?
natka813 [3]
C
No explanation needed
5 0
3 years ago
Read 2 more answers
Find the of x in each triangle.
zhannawk [14.2K]
I pretty sure you either add or subtract to get the answer
7 0
3 years ago
Read 2 more answers
Solve equation y+5=-12
DochEvi [55]

Hope this helps :).                                

4 0
3 years ago
Read 2 more answers
Let f(x)=2x-6. Solve f^-1(x) when x=2<br> -5<br> 4<br> -2<br> 7
ladessa [460]

Answer:

4.

Step-by-step explanation:

f^-1(x) is the inverse of f(x). That means that f(x) = 2x - 6 becomes...

x = 2y - 6

2y - 6 = x

2y = x + 6

y = 1/2x + 3.

When x = 2...

y = 1/2(2) + 3

= 1 + 3

= 4.

Hope this helps!

6 0
3 years ago
Look below for the question. Rearrange them in order.
IgorLugansk [536]
Go ahead and do your own work buddy that’s how you learn shisjdjdhdifndkdnebe
8 0
3 years ago
Other questions:
  • Ignoring color, what kind of symmetry does the pinwheel have? A. rotational symmetry B. line symmetry C. both rotational and lin
    10·1 answer
  • If the area of the following parallelogram is 30 square centimeters, what is the length of the base?
    14·2 answers
  • Two systems of equations are shown below: system a system b 6x y = 2 2x − 3y = −10 −x − y = −3 −x − y = −3 which of the followin
    13·2 answers
  • I kinda get this problem but i just want to see what other answers people got to see if i did the question wrong.
    12·2 answers
  • Fractions on a Number line. Use: 1/3 , 3/3, 8/4, 5/6, 2/8, 1 2/3
    5·1 answer
  • Does 22km 22m = 2222m
    13·1 answer
  • Simplify 5- (-2x – 7)
    9·2 answers
  • Solve (10b+7b^2-6b^3)-(12b^2-3b^3)
    12·1 answer
  • How do you find the value of X? Isosceles and Equilateral Traingle
    13·2 answers
  • The point A(−7,−3) is reflected over the point (−1,−4) and its image is point B. What are the coordinates of point B?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!