Step 1- Hypotheses -: Null hypothesis H,: u = 500 (or) The population average weight of tablets is equal to 500 mg Alternative hypothesis H;: u# 500 (or) The population average weight of tablets is not equal to 500 mg Step 2- Calculation of z test statistic: Given values are, x bar = sample mean = 504.5 mg H = population mean = 500 mg o = Population standard deviation =6 [ because population variance o = 36] %3D n= sample size = 50 Substitute the above values in z test statistic formula as given = z vn 504.5-500 4.5 6/7.071 4.5 0.85 5.30 Thus, the z test statistic is 5.30

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Question

A company manufacturing some medicine tablets with the Average weight of 500 mg and population variance of 36 mg. A quality officer in a company wants to investigate whether the weight of Paracetamol tablets is differed from 500 mg. To investigate He taken 50 tablets at the time of manufacturing and find that the average weight of 50 tablets is 504.5 mg. 

Make the hypothesis test that the average weight of tablets is differ from or not at 95% confidence level. 


Note:
The exercise is already answered, but gives an extensive explanation of the results obtained.

-Please, preferably, in digital format the answer, sometimes I don't understand very well when it is done by hand.

Step 1- Hypotheses -:
Null hypothesis H,: u = 500 (or) The population average weight of tablets is equal to 500 mg
Alternative hypothesis H;: u# 500 (or) The population average weight of tablets is not equal to 500 mg
Step 2- Calculation of z test statistic:
Given values are,
x bar = sample mean = 504.5 mg
H = population mean = 500 mg
o = Population standard deviation =6 [ because population variance o = 36]
%3D
n= sample size = 50
Substitute the above values in z test statistic formula as given
= z
vn
504.5-500
4.5
6/7.071
4.5
0.85
5.30
Thus, the z test statistic is 5.30
Transcribed Image Text:Step 1- Hypotheses -: Null hypothesis H,: u = 500 (or) The population average weight of tablets is equal to 500 mg Alternative hypothesis H;: u# 500 (or) The population average weight of tablets is not equal to 500 mg Step 2- Calculation of z test statistic: Given values are, x bar = sample mean = 504.5 mg H = population mean = 500 mg o = Population standard deviation =6 [ because population variance o = 36] %3D n= sample size = 50 Substitute the above values in z test statistic formula as given = z vn 504.5-500 4.5 6/7.071 4.5 0.85 5.30 Thus, the z test statistic is 5.30
Step 3:z-table value:
Given Significance level is a = 0.05.
Now, Za/z is the z critical value at 95% confidence level is +1.96 (refer from the standard normal z table values
i.e., za/2- Z0.05/2 =+1.96
step 4 - Rejection rule:
we rejecting null hypothesis H, if z test statistic value outside the range of z critical values. otherwise accept
null hypothesis H, at 95% confidence level.
Step 5 - Conclusion:
Since, the z test statistic (5.30) is outside the z critical values of (-1.96 to +1.96). Thus, we have sufficient
evidence to reject the null hypothesis H, at 95% confidence level.
Hence, null hypothesis H, is rejected. So, the average weight of tablets is not equal to 500 mg
Transcribed Image Text:Step 3:z-table value: Given Significance level is a = 0.05. Now, Za/z is the z critical value at 95% confidence level is +1.96 (refer from the standard normal z table values i.e., za/2- Z0.05/2 =+1.96 step 4 - Rejection rule: we rejecting null hypothesis H, if z test statistic value outside the range of z critical values. otherwise accept null hypothesis H, at 95% confidence level. Step 5 - Conclusion: Since, the z test statistic (5.30) is outside the z critical values of (-1.96 to +1.96). Thus, we have sufficient evidence to reject the null hypothesis H, at 95% confidence level. Hence, null hypothesis H, is rejected. So, the average weight of tablets is not equal to 500 mg
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON