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
baherus [9]
3 years ago
5

⦁ In a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football. Construct a 95% confiden

ce interval for the proportion of adults in the United States whose favorite sport to watch is football.
Mathematics
1 answer:
fomenos3 years ago
5 0

Answer:

95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].

Step-by-step explanation:

We are given that in a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football.

Firstly, the pivotal quantity for 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is given by;

        P.Q. = \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } ~ N(0,1)

where, \hat p = proportion of adults in the United States whose favorite sport to watch is football in a sample of 1219 adults = \frac{354}{1219}

           n = sample of US adults  = 1291

           p = population proportion of adults

<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5%

                                                    significance level are -1.96 & 1.96}

P(-1.96 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 1.96) = 0.95

P( -1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } < {\hat p-p} < 1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } ) = 0.95

P( \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } < p < \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } ) = 0.95

<u>95% confidence interval for p</u> = [ \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } , \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } ]

                         = [ \frac{354}{1219}-1.96 \times {\sqrt{\frac{\frac{354}{1219}(1-\frac{354}{1219})}{1219} } , \frac{354}{1219}+1.96 \times {\sqrt{\frac{\frac{354}{1219}(1-\frac{354}{1219})}{1219} } ]

                         = [0.265 , 0.316]

Therefore, 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].

You might be interested in
Leah has sold magazine subscriptions worth $330 for a school fundraiser. If she reaches a total of $500, she wins a gift certifi
insens350 [35]
You can solve by subtracting: 500-330

but I like to use mental math and think this way:
she has 330
70 more will give her 400
and 100 more will give her 500
100 + 70 is 170.
7 0
3 years ago
13 feet in 5 steps plss
Mashutka [201]

Answer:

2.6 feet per step

Step-by-step explanation:

8 0
2 years ago
identify the type of sampling used​ (random, systematic,​ convenience, stratified, or cluster​ sampling) in the situation descri
sertanlavr [38]

Answer: Random sampling

Step-by-step explanation:

  • A random sampling technique is a method of sampling in which each member for the sample is chosen randomly from the population.
  • Systematic sampling :  It is a kind of random sampling in which the members get selected after a fixed interval but a random starting point.
  • Convenience sampling : It is a kind of random sampling in which the members get selected on the basis of researchers convenience.
  • Stratified sampling :  It is a kind of random sampling in which the entire population is divided into a finite number of strata , the researcher select members for sample from each strata.
  • Cluster sampling : It is a kind of random sampling in which the entire population is divided into clusters. Then a random sample of cluster is drawn by researcher.

In the given situation , 784 adults are selected after their telephone numbers were randomly generated by a​ computer.

Therefore , the  type of sampling used​ here is :  random sampling

7 0
3 years ago
Heccin hurry
Semenov [28]

Answer:

<h2>x = 2</h2>

Step-by-step explanation:

Given the equation model 4x+(-4) = -2x+8

To find the value of x, the following steps must be followed

4x+(-4) = -2x+8\\4x-4 = -2x+8\\subtracting\ 8\ from\ both\ sides\\4x-4-8=-2x+8-8\\4x-12=-2x\\4x+2x=12\\6x=12\\x=\frac{12}{6}\\ x = 2

The value of x is 2

6 0
2 years ago
Read 2 more answers
A line that passes through two sides of a triangle divides the sides proportionally.
vlada-n [284]
It's B I got it right on my test
4 0
3 years ago
Other questions:
  • Round 38.7 too ok the nearest whole. Use place value understanding and a number line to show your thinking
    5·2 answers
  • The ABC Automobile Company assembles cars, but buys it’s parts from another company. The company buys tires from a wholesaler th
    15·1 answer
  • How do you get figure 1 to 2?
    7·1 answer
  • How many even, three-digit positive integers have the property that two of the digits are equal, but not all three are equal?
    12·1 answer
  • I literally have no idea how to do this help...
    10·2 answers
  • A swimming pool's large drain will empty the pool in 3 hours while its smaller drain takes 6 hours. If both drains are opened, h
    6·2 answers
  • Mrs. Pregnals's biology classes are going on a field trip. She has them break into groups of three or four
    15·1 answer
  • Help anyone, would be nice!
    11·1 answer
  • Trevor recorded the amount of material collected for recycling at his school for 5
    15·1 answer
  • What i the solution to this equation<br> 6 (x - 5) = 4x + 20
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!