The tables you are given to use are “cumulative”. This means that they measure the probability from the lowest end of the distribution up to the z score you look up on the table. this looks like this…

This looks VERY different from the confidence interval we want to represent…

So HOW do we use the negative table in answering this question? Well if the confidence interval is 99%, then that leaves a total of 1% outside of the interval, and the outside of the interval is divided equally between the upper and lower tails as illustrated here:

…So now if I want to look up the value of z on the table, the easiest way to do so is to look up the z score associated with the area of 0.005 located in the lower tail – on the negative z-table.

The video shows that the proper z-value from the table that cuts off the lower 0.005 of a distribution is z = -2.575

Hello Jason,
in question 2 d and e it says to interpret. It is not clear to me wheather the answer to this question is in you showing how the confidence interval gets wider or like in question b we have to write that paragraph about repeatedly taking samples?

You are correct Mohamed. I was working to make it clear how the confidence interval width is affected by choosing different confidence levels (in the case of part d) or changing the sample size (part e), but all that would be required for answering an exam question like this would be to say the following:

2d)
We estimate that the mean falls between 6.2533 and 6.7468, and this type of estimation is correct 90% of the time.

2e)
We estimate that the mean falls between 6.3303 and 6.6697, and this type of estimation is correct 95% of the time.

Hi Jason,
How come it is not “if we repeatedly took sample sizes of n=100…” – how do we know when that answer is necessary and when it is good enough to just say “99% of the time, this estimation is correct…”
Because question 2b) says interpret the 95% confidence interval and 2d) 90% confidence interval estimate – is that what the sign is to tell us which answer they want?

You should include ““if we repeatedly took sample sizes of n=…” with any interpretations of confidence intervals. If there is a place that I did not, then I was being a bit lazy. Let me know and I’ll correct it.

WHy are we using the negative table instead of positive?

The tables you are given to use are “cumulative”. This means that they measure the probability from the lowest end of the distribution up to the z score you look up on the table. this looks like this…

This looks VERY different from the confidence interval we want to represent…

So HOW do we use the negative table in answering this question? Well if the confidence interval is 99%, then that leaves a total of 1% outside of the interval, and the outside of the interval is divided equally between the upper and lower tails as illustrated here:

…So now if I want to look up the value of z on the table, the easiest way to do so is to look up the z score associated with the area of 0.005 located in the lower tail – on the negative z-table.

The video shows that the proper z-value from the table that cuts off the lower 0.005 of a distribution is z = -2.575

Hello Jason,

in question 2 d and e it says to interpret. It is not clear to me wheather the answer to this question is in you showing how the confidence interval gets wider or like in question b we have to write that paragraph about repeatedly taking samples?

You are correct Mohamed. I was working to make it clear how the confidence interval width is affected by choosing different confidence levels (in the case of part d) or changing the sample size (part e), but all that would be required for answering an exam question like this would be to say the following:

2d)We estimate that the mean falls between 6.2533 and 6.7468, and this type of estimation is correct 90% of the time.

2e)We estimate that the mean falls between 6.3303 and 6.6697, and this type of estimation is correct 95% of the time.

Thank you Very clear.

Hi Jason,

How come it is not “if we repeatedly took sample sizes of n=100…” – how do we know when that answer is necessary and when it is good enough to just say “99% of the time, this estimation is correct…”

Because question 2b) says interpret the 95% confidence interval and 2d) 90% confidence interval estimate – is that what the sign is to tell us which answer they want?

You should include ““if we repeatedly took sample sizes of n=…” with any interpretations of confidence intervals. If there is a place that I did not, then I was being a bit lazy. Let me know and I’ll correct it.