hypothesis Testing with only &gt; Mean side of z table

Original post by ryannixon

cant quite get my head round how to work out the significance level on my question. On my z table it goes from TOP - 0-0.09 in 0.01 increments and LEFT-SIDE 0-4 in 0.1. Completing a one tailed test the critical value I have read says 1.645 so do i go to 1.645 on my z table and get the data or am I looking for 0.05 or close to inside the z table and thats my critical value? thanks

** 1.645 on my z table corresponds in-between 0.4495 &
0.45053

and inside the table 0.05 corresponds to in-between 0.02 & 0.03 on the columns and rows

Can you post the original question / your working? Im a bit confused by your description. Also, why do you have to use a table, most people use a calc these days.

I suspect if its a one sided 5% test youd add 0.5 to your values and you read the z table as
1.6xx row
.04x column
and interpolate the 0.005 value (adjacent column) as you seem to be doing, so something like
https://www.simplypsychology.org/z-table.html

(edited 2 months ago)

Reply 2

OP

The Quality Assurance Department is anxious to improve the nominal value of the capacitors to ensure more of
them fall within the rated tolerance band. The manufacturing process is adjusted in an attempt to bring about
this improvement. Following the adjustment, a further sample of 100 capacitors is taken in order to determine
if the adjustment has resulted in an improvement to the nominal value of the capacitors. Analysing this second
sample, it is noted that the mean value is now 46.5 μF, with a standard deviation of 2 μF.
By comparing these new results of the capacitor values following the manufacturing adjustment, with the
values obtained in part (c) recorded before the adjustment, show whether or not you agree with the
hypothesis that the adjustment to the manufacturing process has had a beneficial effect by making the
capacitor values closer to the desired manufactured nominal value of 47 μF.

Reply 3

Original post by ryannixon

The Quality Assurance Department is anxious to improve the nominal value of the capacitors to ensure more of
them fall within the rated tolerance band. The manufacturing process is adjusted in an attempt to bring about
this improvement. Following the adjustment, a further sample of 100 capacitors is taken in order to determine
if the adjustment has resulted in an improvement to the nominal value of the capacitors. Analysing this second
sample, it is noted that the mean value is now 46.5 μF, with a standard deviation of 2 μF.
By comparing these new results of the capacitor values following the manufacturing adjustment, with the
values obtained in part (c) recorded before the adjustment, show whether or not you agree with the
hypothesis that the adjustment to the manufacturing process has had a beneficial effect by making the
capacitor values closer to the desired manufactured nominal value of 47 μF.

And how did you come up with the 1.645 value? Im presuming there is a previous question part where they talk about a first sample, which you compare with?

Reply 4

OP

I have read that when doing a one tailed z test the critical value is 1.645. I suppose I'm asking whether I use the 0.05 from the significance level and get the critical value from that?

The z table I have been provided 0.05 is in-between 0.02 and 0.03
0.02 - 0.04776
0.03 - 0.05172

Reply 5

OP

Original post by mqb2766

And how did you come up with the 1.645 value? Im presuming there is a previous question part where they talk about a first sample, which you compare with?

the first sample asks you to work out the z score under the curve between 42-50 microfarads to find out the amount of capacitors likely to fall in the allowed tolerance from the 500 samples

Reply 6

Original post by ryannixon

I have read that when doing a one tailed z test the critical value is 1.645. I suppose I'm asking whether I use the 0.05 from the significance level and get the critical value from that?

The z table I have been provided 0.05 is in-between 0.02 and 0.03
0.02 - 0.04776
0.03 - 0.05172

1.645 corrresponds to a one tailed 5% significance test.

Otherwise Im not really sure what youre doing.

Reply 7

OP

Original post by mqb2766

Original post by ryannixon

I have read that when doing a one tailed z test the critical value is 1.645. I suppose I'm asking whether I use the 0.05 from the significance level and get the critical value from that?

The z table I have been provided 0.05 is in-between 0.02 and 0.03
0.02 - 0.04776
0.03 - 0.05172

1.645 corrresponds to a one tailed 5% significance test.

Otherwise Im not really sure what youre doing.

I was just confused because the z table provided only shows from 0 to 0.49998 and was trying to find the significance level within that table

Reply 8