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lina2011 [118]
2 years ago
10

A CBS News/New York Times opinion poll asked 1,190 adults whether they would prefer balancing the federal budget over cutting ta

xes; 59% of those asked said "yes." Suppose that in fact 62% of all adults favor balancing the budget over cutting taxes. If this poll was not biased, what is the probability you would get p^=0.59 or less?
Mathematics
1 answer:
nikklg [1K]2 years ago
7 0

Using the <u>normal distribution and the central limit theorem</u>, it is found that there is a 0.0166 = 1.66% probability of a sample proportion of 0.59 or less.

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.  
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sampling proportions of a proportion p in a sample of size n has mean \mu = p and standard error s = \sqrt{\frac{p(1 - p)}{n}}

In this problem:

  • 1,190 adults were asked, hence n = 1190
  • In fact 62% of all adults favor balancing the budget over cutting taxes, hence p = 0.62.

The mean and the standard error are given by:

\mu = p = 0.62

s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.62(0.38)}{1190}} = 0.0141

The probability of a sample proportion of 0.59 or less is the <u>p-value of Z when X = 0.59</u>, hence:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.59 - 0.62}{0.0141}

Z = -2.13

Z = -2.13 has a p-value of 0.0166.

0.0166 = 1.66% probability of a sample proportion of 0.59 or less.

You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213

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svlad2 [7]

Answer:

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Step-by-step explanation:

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4 0
3 years ago
A manufacturer of running shoes knows that the average lifetime for a particular model of shoes is 15 months. Someone in the res
AveGali [126]

Answer:

The decision rule is  

Fail to reject the null hypothesis

 The conclusion is  

There is no sufficient evidence to show that  the  designer's claim of a better shoe is supported by the trial results.

Step-by-step explanation:

From the question we are told that

  The population mean is  \mu = 15 \ months

   The sample size is  n =  25

   The sample mean is  \= x  = 17 \ months

   The standard deviation is  s = 5.5 \ months

Let assume the level of significance of this test is  \alpha  = 0.05

    The null hypothesis is  H_o :  \mu = 15

     The alternative hypothesis is  H_a : \mu  > 17

Generally the degree of freedom is mathematically represented as  

         df = n -1

=>       df = 25 -1

=>       df = 24

Generally the test statistics is mathematically represented as

        t = \frac{\= x- \mu }{\frac{s}{\sqrt{n} } }

=>   t = \frac{ 17 - 15 }{\frac{5.5}{\sqrt{25} } }

=>   t =  1.8182

Generally from the student t distribution table the probability of obtaining   t =  1.8182 to the right of the curve at a degree of freedom of df = 24  is  

    p-value  = P(t > 0.18182 ) = 0.4286

From the value obtained we see that  p-value > \alpha hence

The decision rule is  

Fail to reject the null hypothesis

 The conclusion is  

There is no sufficient evidence to show that  the  designer's claim of a better shoe is  supported by the trial results.

7 0
2 years ago
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed th
dexar [7]
\tan(51^o 33')=  \frac{200}{base1}
<span>
base1= 158.802

</span>\tan(18^o 33')= \frac{200}{base2}
<span>
base2=596.008

the distance travelled = 596.008 - 158.802 = 438 m</span>

8 0
3 years ago
Which graph represents the solution set of this inequality?<br> -3b - 15 &gt; -24
Natasha2012 [34]

Answer:

A

REASON:

It's not B or D because it's increasing and it's not C because if -3 - 15 is -18 then I am pretty sure it's not going to be 3 because it's multiplying  

3 0
3 years ago
Read 2 more answers
How to solve 4k-1.5k=50
padilas [110]
Combine like terms-- you can combine the k's:
4k-1.5k=2.5k

Now you have:
2.5k=50

Simply divide both sides by 2.5 to find the value of k:
\frac{2.5k}{2.5}=\frac{50}{2.5}\\\\k=20
6 0
3 years ago
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