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
laiz [17]
3 years ago
5

A physical education teacher wanted to test whether her county’s students are falling below the national proportion. It is known

that the national proportion for high school juniors passing the aerobic portion of the test (running a mile in less than 10 minutes) is 0.70. Using α = 0.05, is there sufficient evidence to conclude that less than 70% of students run one mile in less than 10 minutes? Conduct a full hypothesis test by following the steps below.
a. Define the population parameter in context in one sentence.
b. State the null and alternative hypotheses using correct notation.
c. State the significance level for this problem.
d. Check the three conditions of the Central Limit Theorem that allow you to use the one- proportion z-test using one complete sentence for each condition. Show work for the numerical calculation. You can assume the population is large.
e. Calculate the test statistic "by-hand." Show the work necessary to obtain the value by typing all the steps needed and the resulting test statistic. Do not round while doing the calculation. Then, round the test statistic to decimal places.
f. Calculate the p-value using the standard Normal table and provide the answer. Use four decimal places for the p-value.
g. State whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence.
h. Based on your above decision, state your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences.
Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
7 0

Answer:

(a) The population parameter is students who ran the mile in less than 10 minutes.

(b) The hypothesis being tested is:

H0: p = 0.70

Ha: p < 0.70

(c) The significance level is 0.05.

(d) In order to conduct a one-sample proportion z-test, the following conditions should be met:

The data are a simple random sample from the population of interest.

The population is at least 10 times as large as the sample.

n⋅p ≥ 10 and n⋅(1−p) ≥ 10, where n is the sample size and p is the true population proportion.

n⋅p = 756 * 0.70 ≥ 10

n⋅(1−p) = 756 * (1 - 0.70) ≥ 10

All the conditions are met.

(e) p = 504/756 = 0.67

The test statistic, z = (p - p)/√p(1-p)/n = (0.67 - 0.70)/√0.70(1-0.70)/756 = -2.00

(f) The p-value is 0.0228.

(g) Since the p-value (0.0228) is less than the significance level (0.05), we can reject the null hypothesis.

(h) Therefore, we can conclude that less than 70% of students run one mile in less than 10 minutes.

Step-by-step explanation:

You might be interested in
Can you do question c for me?
Sveta_85 [38]

Answer:

28.2

Step-by-step explanation:

91 × 18 = 1638

1638 ÷ 58 = 28.2413793103

rounded to 1 significant figure = 28.2 as 4 rounds down

hope this helps

7 0
3 years ago
A basketball player makes 30% of her foul shots. she shoots 5 foul shots. you are interested in the number of shots that she mak
vampirchik [111]
This would be a binomial model, since there is a fixed number of trials, the probabilities are independent and there are only two choices (either the shot is made or missed).
5 0
3 years ago
Brainles app doesn’t nothing to help me
castortr0y [4]

Answer:

true but can u help me or u can go to questioncove its better then branily but can u help me pls

Step-by-step explanation:

3 0
3 years ago
The endpoints of EF¯¯¯¯¯¯¯¯ are E(−4,12) and F(3,15). Find the coordinates of the midpoint M..
Ray Of Light [21]

Answer:

(-1/2, 27/2)

Step-by-step explanation:

Midpoint formula: (x^1 +x^2/ 2, y^1 +y^2/ 2)

(-4 +3 /2, 12+15/ 2) -> (-1/2, 27/2)

5 0
2 years ago
Are all squares simular true or false
enyata [817]
ANSWER:
true


STEP-BY-STEP EXPLANATION:
5 0
3 years ago
Other questions:
  • The four people at Carla's birthday will get one-quarter (one fourth) of the cake each. Carla puts 16 candies on the cake so tha
    7·2 answers
  • How to find the angles of a circle?
    11·1 answer
  • T(z)=z-8 <br> Evaluate t(-2)
    6·1 answer
  • Calculate the exact lengths of segment e and segment f. Which is longer?
    7·1 answer
  • SOMEONE HELP ME ASAP!!!!!!
    12·1 answer
  • Can someone help me out with this question??? ​
    12·1 answer
  • Evaluate f(x)= - 3 x - 8; find f(-4)<br><br><br> please answer
    10·2 answers
  • What is the value of x
    14·2 answers
  • Carl is seventy-three inches tall. This is twenty-one inches less than two times Marcia's height. How tall is Marcia?
    12·2 answers
  • Jean bought 7 melons.<br> Each melon weighs 23 pound.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!