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
dezoksy [38]
2 years ago
10

A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked whether or not during the

past 30 days they had used their phone while in a store to call a friend or family member for advice about a purchase they were considering. The poll surveyed 1024 adults living in the United States by telephone. Of these, 471 responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering. (a) Find (plusminus 0.0001) SE_p the sample proportion, the standard error of the sample proportion, and the margin of error for 95% confidence. p = SE_p = m = (b) Find the 95% large-sample confidence interval (plusminus 0.001) for the population proportion, the 95% large-sample confidence interval is from ____ to _____.
Mathematics
1 answer:
EastWind [94]2 years ago
8 0

Answer:

a) \hat p=\frac{471}{1024}=0.460

The standard error is given by:

SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156

And the margin of error is given by:

ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305

b) The 99% confidence interval would be given by (0.429;0.491)

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Data given and notation  

n=1024 represent the random sample taken    

X=471 represent the people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

\hat p=\frac{471}{1024}=0.460 estimated proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering    

p= population proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

Part a

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=1.96

The standard error is given by:

SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156

And the margin of error is given by:

ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305

Part b

If we replace the values obtained we got:

0.460-1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.429

0.460+1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.491

The 99% confidence interval would be given by (0.429;0.491)

You might be interested in
What is 6×9÷18+100-11+4
mojhsa [17]

6 × 9 ÷ 18 + 100 - 11 + 4

Use the order of operations to simplify:

  • Parentheses
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction

6 × 9 ÷ 18 + 100 - 11 + 4

There are no parentheses or exponents, so multiplication comes first. Multiply 6 and 9.

54 ÷ 18 + 100 - 11 + 4

Next is division. Divide 54 by 18.

3 + 100 - 11 + 4

Finally, add and subtract from left to right.

103 - 11 + 4

92 + 4

96

<h3>Answer:</h3>

96

4 0
3 years ago
In the data set below, which of these points is most likely and outlier?
shusha [124]
<h2>Answer:</h2>

Option: D is the correct answer.

                 D.  (2,54)

<h2>Step-by-step explanation:</h2>

We know that an outlier of a data set is the value that stands out of the rest of the data point i.e. either it is a too high value or a too low value as compared to other data points.

Here  we are given a set of data points as:

         (2,54)

          (4,7)

         (6, 9)

         (8,12)

         (10,15)

Hence, we see that the output values i.e. 7 in (4,7) ; 9 in (6,9) ; 12 in (8,12) and 15 in (10,15) are closely related.

Hence, the data point that is an outlier is:

                  (2,54)

(As 54 is a much high value as compared to other)

5 0
3 years ago
Which graph represents a function with direct variation?<br><br>​
sweet [91]

This is easier than you think!

When a graph shows direct variation, it always <em>passes through the origin</em>

The origin is (0, 0)

The very <u>center! </u>

Your answer is the first graph!

5 0
3 years ago
Read 2 more answers
A square with one side length represented by an expression is shown below
crimeas [40]
It is mentioned in the problem that the shape is a square, hence, we could say that all side's measurement is the same and it is equal. It can be written in a different arrangement of terms, but still, the value to be solved is the same. The sides can be written in the following forms:
S1=6(3X+8)+32+12X
S2=18X+48+32+12X
S3=18X+80+12X
S4=30X+80
3 0
3 years ago
How many nickels are in one roll of $10
Alona [7]

Answer:

40 Nickels

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • For a cone, if the radius was quadrupled and the slant height was reduced to 1/6 of its original size what would be the formula
    15·1 answer
  • Jenna saved $816 and then she spent $96. Which of the following, is the best estimate, of how much Jenna has left?
    8·2 answers
  • Find the angle(s) that are Alternate Interior to angle 5.
    7·1 answer
  • Please help me divide
    14·2 answers
  • What's the volume of the figure​
    14·2 answers
  • Six values on the number line above are marked with letters. Which letters represent integers when the value on the number line
    12·1 answer
  • An SRS of 2,500 individuals was taken from a large city to estimate the percentage of city residents with a graduate degree. 555
    14·1 answer
  • Does anyone know this
    12·2 answers
  • What are the like terms in the expression?
    6·2 answers
  • Ryan just got hired for a new job and will make $48,000 in his first year Ryan was told that he can expect to get raises of $3,5
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!