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
Natali5045456 [20]
1 year ago
12

Assume that a simple random sample has been selected from a normally distributed population. State the hypotheses, find the test

statistic, critical value(s) , P-value , and state the final conclusion.Test the claim that for the population of female college students, the mean weight is given by μ = 132 lb. Sample data are summarized as n = 20, overbar(x) = 137 lb, and s = 14.2 lb. Use a significance level of α = 0.1.
Mathematics
1 answer:
BaLLatris [955]1 year ago
7 0

Solution

Hypotheses:

- The population mean is 132. In order to test the claim that the mean is 132, we should check for if the mean is not 132.

- Thus, the Hypotheses are:

\begin{gathered} H_0:\mu=132 \\ H_1:\mu\ne132 \end{gathered}

Test statistic:

- The test statistic has to be a t-statistic because the sample size (n) is less than 30.

- The formula for finding the t-statistic is:

\begin{gathered} t=\frac{\bar{X}-\mu}{\frac{s}{\sqrt{n}}} \\  \\ where, \\ \bar{X}=\text{ Sample mean} \\ \mu=\text{ Population mean} \\ s=\text{ Standard deviation} \\ n=\text{ Sample size} \end{gathered}

- Applying the formula, we have:

\begin{gathered} t=\frac{137-132}{\frac{14.2}{\sqrt{20}}} \\  \\ t=\frac{5}{3.1752} \\  \\ t\approx1.5747 \end{gathered}

Critical value:

- The critical value t-critical, is gotten by reading off the t-distribution table.

- For this, we need the degrees of freedom (df) which is gotten by the formula:

\begin{gathered} df=n-1 \\ df=20-1=19 \end{gathered}

- And then we also use the significance level of 0.1 and the fact that it is a two-tailed test to trace out the t-critical. (Note: significance level of 0.1 implies 10% significance level)

- This is done below:

- The critical value is 1.729

P-value:

- To find the p-value, we simply check the table for where the t-statistic falls.

- The t-statistic given is 1.5747. We simply check which values this falls between in the t-distribution table. It falls between 1.328 and 1.729. We can simply choose a value between 0.1 and 0.05 and multiply the result by 2 since it is a two-tailed test.

- However, we can also use a t-distribution calculator, we have:

- Thus, the p-value is 0.13183

Final Conclusion:

- The p-value is 0.13183, and comparing this to the significance level of 0.1, we can see that 0.13183 is outside the rejection region.

- Thus, the result is not significant and we fail to reject the null hypothesis

You might be interested in
Given the diagram below find the value of x if the area is 21 aquare meters
Oksanka [162]

Answer:

The answer is <u><em>7</em></u>!

Step-by-step explanation:

(x-4) (x) = 21, x^2 - 4x = 21, x^2 - 4x - 21 = 0, (x - 7) (x + 3) = 0, x = 7 and -3; x can't be negative so the answer is 7!

x = 7 and x - 4 (other side) = 3

5 0
2 years ago
Three equivalent ratio of 48:36
Andre45 [30]
Three equivalent ratios of 48:36 are 12:9 ,24:18 ,16:12.
5 0
3 years ago
Darius buys a bottle of a chemical solution that contains 70% alcohol. The bottle contains 500 ml of solution. How many millilli
mars1129 [50]
It is. 7.17285714285714 you can stop at the thousands
8 0
2 years ago
Read 2 more answers
Which of the following shows the equation log2 8 = 3 written in exponential form?
Kobotan [32]
IT IS A HOPE THIS HELPS!!!
srry 4 caps
3 0
3 years ago
Read 2 more answers
Enter the slope-intercept equation for the image of line ℓ after a clockwise rotation of 90°. (Hint: To find the image of line ℓ
Free_Kalibri [48]

Answer:

y = -2x - 2

Step-by-step explanation:

From the graph attached,

If the line 'l' passes through two points A(0, -1) and B(4, 1).

Rule for the rotation of any point (x, y), 90° clockwise about the origin is,

(x, y) → (y, -x)

By this rule,

A(0, -1) → A'(-1, 0)

B(4, 1) → B'(1, -4)

Let the equation of the line A'B' is,

y - y' = m(x - x')

where m = slope of the line A'B'

And (x', y') is a point lying on the line.

Slope of the line passing through A' and B' will be,

m = \frac{y_2-y_1}{x_2-x_1}

m = \frac{0+4}{-1-1}

m = -2

Therefore, equation of the line passing through (-1, 0) and slope = -2,

y - 0 = (-2)(x + 1)

y = -2x - 2

So the equation of the line after rotation of lie 'l' by 90° clockwise will be,

y = -2x - 2

7 0
2 years ago
Other questions:
  • Which statements are true about a rectangular pyramid with a height of 9 centimeters and a base with the dimensions of 4 centime
    10·2 answers
  • What numbers can I multiply to get 24 and add to get negative 4
    9·2 answers
  • I thought of a number. My number multiplied by 7 is 6 bigger than 50. Find my number.
    11·2 answers
  • Please help me with math thanks
    6·1 answer
  • What is the distance between -2 and 5
    9·1 answer
  • Area in sq. in. = 3/5 in. X 3 1/2 in.
    15·1 answer
  • A scientist needs 80 liters of a 30% solution of alcohol. She has a 20% solution and a 60% solution available.
    6·1 answer
  • What are reactants in the process of photosynthesis check <br> all that apply
    11·1 answer
  • PROBLEM: Riley has a rectangular shaped patio that is 13 feet long by 15 feet wide. He wants to DOUBLE THE AREA of the patio by
    7·1 answer
  • Find an equation for the line below
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!