# Calculating Listeners Tuning in 8-9am: Least/Greatest #s

• MHB
• markosheehan
In summary: So I do not need to use the standard deviation to get the answer. I can just use the 1/✓n formula?Yes, for this problem you can use the 1/✓n formula to get the answer. The standard deviation formula would only be necessary if we were given the SD of the population, but since we are only given the sample size, we can use the 1/✓n formula.
markosheehan
a radio station claims 55% of all listeners tune into their program between 8 and 9 am. To check this claim a competing radio station does a survey of a random sample of listeners in the 8 to 9 am time slot. the survey indicates the claim can not be rejected. if the sample size is 1000 people determine the least and greatest number of listeners that could of said they listen to the radio station.

this is what i have tried but i am not getting the right answer.

p=.55

using the margin of error formula. 1/ √1000 = .03126
so I would of thought the answer would be 1.55 +/- .03126 multiplied by a thousand. this does not give the right answer. the right answer is 519 to 581

markosheehan said:
a radio station claims 55% of all listeners tune into their program between 8 and 9 am. To check this claim a competing radio station does a survey of a random sample of listeners in the 8 to 9 am time slot. the survey indicates the claim can not be rejected. if the sample size is 1000 people determine the least and greatest number of listeners that could of said they listen to the radio station.

this is what i have tried but i am not getting the right answer.

p=.55

using the margin of error formula. 1/ √1000 = .03126
so I would of thought the answer would be 1.55 +/- .03126 multiplied by a thousand. this does not give the right answer. the right answer is 519 to 581

Hi markosheehan,

So this question basically comes down to finding a reasonable interval that we would expect the numbers to fluctuate between. This is often called a "confidence interval" and corresponds to a "fail to reject region" of the null hypothesis. I'm not sure how the material is being presented in your course but can you tell me how you've been told to apply the margin of error formula?

Basically no matter what this is going to look like this: $555 \pm \text{noise}$. Different teachers and courses approach this differently so I'm curious as to what you've been told to do. The answer you provided is not symmetric. Can you confirm that the answer should be 519 to 581? If it were 529 to 581 then that would be symmetric, that is $555 \pm 26$.

519, 581 is the answer at the back of the book.

Usually we use the margin of error formula
E=1/✓n

We have also used the margin of error (for c% confidence interval) E=z* standard deviation of proportion where z is 1.96 at the 95 % confidence. I'm not too sure how this formula works or what it is even used for. But anyway it can not be used here due to the reason we are not given the standard deviation of the population.

markosheehan said:
519, 581 is the answer at the back of the book.

Usually we use the margin of error formula
E=1/✓n

We have also used the margin of error (for c% confidence interval) E=z* standard deviation of proportion where z is 1.96 at the 95 % confidence. I'm not too sure how this formula works or what it is even used for. But anyway it can not be used here due to the reason we are not given the standard deviation of the population.

We don't know the standard deviation of the population, but we do know that SD of the sample. See this page. It looks like this isn't the way you are going though for this homework.

$$\displaystyle \left(55 \pm \frac{1}{\sqrt{1000}} \right) \times 1000 = (519,581)$$

So actually you had it right the first time. :)

thanks

## 1. What is the purpose of calculating listeners tuning in 8-9am?

The purpose of calculating listeners tuning in 8-9am is to determine the number of people who are listening to a specific radio station or program during this time slot. This information can be used by radio stations to measure their audience reach and make decisions about programming and advertising.

## 2. How is the number of listeners tuning in 8-9am calculated?

The number of listeners tuning in 8-9am is calculated by using listener data collected through surveys, ratings, or electronic tracking devices. This data is then analyzed and averaged to determine the estimated number of listeners during this time period.

## 3. What is the significance of the least and greatest numbers in calculating listeners tuning in 8-9am?

The least and greatest numbers in calculating listeners tuning in 8-9am represent the minimum and maximum estimated number of listeners during this time period. These numbers can provide valuable insights into the popularity and reach of a radio station or program.

## 4. How accurate are the calculations of listeners tuning in 8-9am?

The accuracy of the calculations of listeners tuning in 8-9am depends on the quality of the data used and the methodology of the calculation. Generally, these calculations have a margin of error and should be interpreted as estimates rather than precise numbers.

## 5. Why is 8-9am chosen as the time period for calculating listeners?

8-9am is a commonly chosen time period for calculating listeners because it is a peak listening time for many people, particularly during their morning commute. This time period can provide valuable insights into the overall audience reach of a radio station or program.