Mathematics, 06.06.2020 02:01 potato3999

A recent survey collected information on television viewing habits from a random sample of 1,000 people in the United States. Of those sampled, 37 percent indicated that their favorite sport to watch on television was American football. Construct and interpret a 95 percent confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football. Based on your answer to the previous problem, is it reasonable to believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football

Answers: 1

Show answers

Answers

Answer from: bmartinez26

The 95% Confidence Interval we will found for given case is:

(0.34, 0.40)

It is Not reasonable to believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football

Given that:Total size of sample = n = 1000Percent of people in sample indicating that their favorite sport on TV is to watch American football = p = 37% = 0.37 probability.To find:

95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football.

Finding the Confidence Interval:

When there is n sample size and the probability of success is p with level of significance $\alpha$ calculated as:

$CI = p \pm z_0 \sqrt{\dfrac{p(1-p)}{n}$

Where z_0 is the z score $1- \dfrac{\alpha}{2}$ .

1 - $\alpha$ = 0.95 ( since it is given to find 95% CI)

Thus, $\alpha$ = 0.05

The z score at p value = 1 - $\alpha$ /2 = 1 -0.025 = 0.975 is 1.96

Thus we have:

$CI = p \pm z_0 \sqrt{\dfrac{p(1-p)}{n}}\\\\CI = 0.37 \pm 1.96 \sqrt{\dfrac{0.37 \times0.63 }{1000}}\\\\CI = 0.37 \pm 1.96 \times 0.0152 = 0.37 \pm 0.03\\$

Lower limit of CI = 0.34 and Upper limit of CI = 0.40.

The case to decide to believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football can be solved as:

33% = 0.33 probability of actually liking watching american probability.

Since 0.33 is lower than the lower limit of CI for 0.37 probability, thus we reject the null hypothesis that both 0.37 and 0.33 are approximately same, and thus decide that it is false that 0.33 percent believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football.

Thus it is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football.

Learn more about Confidence interval here:

link

Answer from: sarahelrod9

The 95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40). This means that we are 95% sure that the true proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is between (0.34 and 0.40).

The lower bound of the confidene interval is higher than 0.33. So it is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football, this estimate should be higher than 33%.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 1000, \pi = 0.37$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so Z = 1.96 .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.37 - 1.96\sqrt{\frac{0.37*0.63}{1000}} = 0.34$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.37 + 1.96\sqrt{\frac{0.37*0.63}{1000}} = 0.40$

Based on your answer to the previous problem, is it reasonable to believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football

Answer from: Quest

$3 \times 4 = 12 \\ 6 \times 8 = 48$ $48 + 12 = 60$ hope it is correct if not i'm srry i tried to

Answer from: Quest

Step 1: 6x-10=1; step 2: 6x=11

Another question on Mathematics

Mathematics, 21.06.2019 15:30

Find the slope of the line below . enter your answer as a fraction or decimal. use a slash mark ( / ) as the fraction bar if necessary

Answers: 3

Answer

Mathematics, 21.06.2019 22:00

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).

Answers: 2

Answer

Mathematics, 21.06.2019 22:40

Find the missing factor. write your answer inexponential form.9^2=9^4×

Answers: 1

Answer

Mathematics, 22.06.2019 03:20

The value of x must be greater than what?

Answers: 1

Answer

You know the right answer?

A recent survey collected information on television viewing habits from a random sample of 1,000 peo...