For this question if we use the proportion values instead of the whole percent value we get a 0._____ answer. Is that fine if we leave it as that 0. number as our LCL and UCL?

How can we differentiate a question estimation question from chapter 10 vs chapter 11. The way the questions are asked seem to be similar – if not the same.

We could, but it would be extra work and is not necessary here. Converting to proportions is only necessary when you are dealing with nominal data (each individual outcome is a category, not a number). The data in this question is interval (each individual outcome is a numerical measure or count), and so we can leave percentages as percentages, or convert to proportion if we choose to.

How do I know it’s interval?

The mention of a mean is the give away. If you have an numerical average given in the question, then each data point must also be numerical , or in other words – interval (you can’t take the average of categories)

So I might be missing something here or drawing a blank but since we were using a negative z-table wouldn’t the 1.96 be a negative value? And how do we know to use that table instead of the positive table (right side values)?

I point out at time 18:00 in the video that it doesn’t matter (positive or negative) because the formula contains the +/- symbol. This means that BOTH signs will be used in the end. The negative will be used in your Lower Confidence Limit, and the positive version of the z score you read from the table will be used in your Upper Confidence Limit.

How do you know to look up the value on the negative side of the table? Again, it doesn’t matter. You would get the same result from both tables, but it’s easier (and faster) to use the negative z table. If instead you chose to use the positive z table then you would have to first calculate that the area on the table = 1 – area in the tail = 1 – 0.025 = 0.975 (not a big deal, but it’s better to avoid extra calculations).

It is only necessary to convert the sample data into proportions when you are working with nominal data. The sample here is comprised of 60 returns. Each return is a numerical value (like 5%, or 12% etc), so the data collected is interval.

By contrast, a sample made up of nominal data has individual results that are NOT numerical values. For example, if I ask people to record their gender, 20% may be male and 80% female, but the INDIVIDUAL observations are male, female, male, male, female, etc. If we are asked to estimate the proportion of males, then we would convert the 20% to 0.20.

so I understand completely how to do the calculations with the information we have been given in the question. The only thing i am really confused about is how do I know when to use the formula provided and the Z table or the T table etc…

The flowchart on my cheat-sheet covers this. If you are given the POPULATION standard deviation, then use z. If not, use t. This assumes that you’re either performing a hypothesis test or an estimation of ONE population MEAN.

where can I find this flow chart?

Hi Jason,

Could you please answer this for me?

For this question if we use the proportion values instead of the whole percent value we get a 0._____ answer. Is that fine if we leave it as that 0. number as our LCL and UCL?

Yes. That is fine to do and is what is expected for proportions.

Hi Jason,

I am confused as to how you got the 95%. Would you be able to explain that please.

Hi. Check time 1:28 in the video. 95% is the confidence level given in the question itself.

Hi Jason,

How can we differentiate a question estimation question from chapter 10 vs chapter 11. The way the questions are asked seem to be similar – if not the same.

Why aren’t u calculating the limits in proportions ? Like using 0.118 instead of 11.8

We could, but it would be extra work and is not necessary here. Converting to proportions is only necessary when you are dealing with nominal data (each individual outcome is a category, not a number). The data in this question is interval (each individual outcome is a numerical measure or count), and so we can leave percentages as percentages, or convert to proportion if we choose to.

How do I know it’s interval?

The mention of a mean is the give away. If you have an numerical average given in the question, then each data point must also be numerical , or in other words – interval (you can’t take the average of categories)

Hey Jason,

So I might be missing something here or drawing a blank but since we were using a negative z-table wouldn’t the 1.96 be a negative value? And how do we know to use that table instead of the positive table (right side values)?

Thanks in advance!

Hi Johnny,

I point out at time 18:00 in the video that it doesn’t matter (positive or negative) because the formula contains the +/- symbol. This means that BOTH signs will be used in the end. The negative will be used in your Lower Confidence Limit, and the positive version of the z score you read from the table will be used in your Upper Confidence Limit.

How do you know to look up the value on the negative side of the table? Again, it doesn’t matter. You would get the same result from both tables, but it’s easier (and faster) to use the negative z table. If instead you chose to use the positive z table then you would have to first calculate that the area on the table = 1 – area in the tail = 1 – 0.025 = 0.975 (not a big deal, but it’s better to avoid extra calculations).

Why is it that we are using 11.8 & 4 instead of the decimal values of the percentages? And is this acceptable in any other case as well?

thanks!

It is only necessary to convert the sample data into proportions when you are working with nominal data. The sample here is comprised of 60 returns. Each return is a numerical value (like 5%, or 12% etc), so the data collected is interval.

By contrast, a sample made up of nominal data has individual results that are NOT numerical values. For example, if I ask people to record their gender, 20% may be male and 80% female, but the INDIVIDUAL observations are male, female, male, male, female, etc. If we are asked to estimate the proportion of males, then we would convert the 20% to 0.20.

Ok Thanks!

hey Jason,

so I understand completely how to do the calculations with the information we have been given in the question. The only thing i am really confused about is how do I know when to use the formula provided and the Z table or the T table etc…

The flowchart on my cheat-sheet covers this. If you are given the POPULATION standard deviation, then use z. If not, use t. This assumes that you’re either performing a hypothesis test or an estimation of ONE population MEAN.