Mathematics, 12.03.2021 20:40 Luis2737

In an article in the Journal of Advertising, Weinberger and Spotts compare the use of humor in television ads in the United States and the United Kingdom. They found that a substantially greater percentage of U. K. ads use humor. (a) Suppose that a random sample of 400 television ads in the United Kingdom reveals that 147 of these ads use humor. Find a point estimate of and a 95 percent confidence interval for the proportion of all U. K. television ads that use humor. (Round your answers to 3 decimal places.) (b) Suppose a random sample of 455 television ads in the United States reveals that 119 of these ads use humor. Find a point estimate of and a 95 percent confidence interval for the proportion of all U. S. television ads that use humor. (Round your answers to 3 decimal places.) (c) Do the confidence intervals you computed in parts a and b suggest that a greater percentage of U. K. ads use humor

Answers: 2

Show answers

Answers

Answer from: jonmorton159

The point estimate is 0.368.

The 95 percent confidence interval for the proportion of all U.K. television ads that use humor is (0.321, 0.415).

The point estimate is 0.262.

The 95 percent confidence interval for the proportion of all U.S. television ads that use humor is (0.222, 0.302).

Yes, because the lower bound of the confidence interval for UK proportions is higher than the upper bound of the confidence interval for US proportions.

Step-by-step explanation:

(a) Suppose that a random sample of 400 television ads in the United Kingdom reveals that 147 of these ads use humor.

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 $1 - \frac{\alpha}{2}$ .

Sample of 400:

This means that n = 400

Point estimate:

$\pi = \frac{147}{400} = 0.368$

The point estimate is 0.368.

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:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.368 - 1.96\sqrt{\frac{0.368*0.632}{400}} = 0.321$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.368 + 1.96\sqrt{\frac{0.368*0.632}{400}} = 0.415$

The 95 percent confidence interval for the proportion of all U.K. television ads that use humor is (0.321, 0.415).

(b) Suppose a random sample of 455 television ads in the United States reveals that 119 of these ads use humor.

Sample of 455:

This means that n = 455

Point estimate:

$\pi = \frac{119}{455} = 0.262$

The point estimate is 0.262.

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:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.262 + 1.96\sqrt{\frac{0.262*0.738}{455}} = 0.222$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.262 + 1.96\sqrt{\frac{0.262*0.738}{455}} = 0.302$

The 95 percent confidence interval for the proportion of all U.S. television ads that use humor is (0.222, 0.302).

Yes, because the lower bound of the confidence interval for UK proportions is higher than the upper bound of the confidence interval for US proportions.

Answer from: Quest

What do you mean by that?

Answer from: Quest

jml angle lkj & angle mj = lm

Another question on Mathematics

Mathematics, 21.06.2019 16:50

The parabola x = y² - 9 opens: a.)up b.)down c.) right d.)left

Answers: 1

Answer

Mathematics, 21.06.2019 19:10

In the triangles, bc =de and ac fe.if the mzc is greater than the mze, then ab isdfelth

Answers: 2

Answer

Mathematics, 21.06.2019 19:30

Look at this pattern ; 1,4,9, number 10000 belongs in this pattern . what’s the place of this number?

Answers: 3

Answer

Mathematics, 21.06.2019 22:00

Astudent has created the give circuit diagram. it consists of a battery, a resistor, and a light bulb. in one minute, 1.2c of charge flows through the resistor. how much charge flows through the light bulb in one minute?

Answers: 1

Answer

You know the right answer?

In an article in the Journal of Advertising, Weinberger and Spotts compare the use of humor in telev...

Questions

Mathematics, 14.09.2019 06:20

Find the values of x and y.(10x – 61)°(18y + 5)°(x + 10)°

Mathematics, 14.09.2019 06:20

Chapter 1 unit pricing and currency7. the cost of a 355-ml can of juice is $1.25 in a vending machine. a 1.89-l carton ofthe same juice co...