Question

7. You standardize an HCl solution and obtain the following values: 0.5026, 0.5029, 0.5031, 0.5045, 0.5025, and 0.5023 M.

a. The 0.5045 data point seems to differ a lot from the others. Use the Q test at 90% confidence and determine whether this point may be discarded. (If so, leave this point out for the rest of the problem.)

b. Determine the mean of the data.

c. Determine the standard deviation.

d. Using the t table, calculate the range of molarities where you can be 95% confident that the true molarity lies for your sample.

Please explain briefly!!!!

Answer 1

Given,

HCl solution and obtain the following values: 0.5026, 0.5029, 0.5031, 0.5045, 0.5025, and 0.5023

a. Arrange them in the ascending order : 0.5023, 0.5025, 0.5026, 0.5029, 0.5031, 0.5045

The suspected value X_N = 0.5045

The nearest Value X_N-1 = 0.5031

First Data point X₁ = 0.5023

Experimental Q-value :

Critical value of Q for 90% for( N=6 ) Q_Crit= 0.560

As Q_Exp(0.6364) > Q_crit ( 0.560) ; the suspected value 0.5045 is  then the suspect value can be characterized as an outlier and it can be discarded.

After the oulier is being discarded;

Remaining 5 data points are

X

0.5023

0.5025

0.5026

0.5029

0.5031

b.Determine the mean of the data

Mean of the Data :

n : Number of Data points = 5

	x
	0.5023
	0.5025
	0.5026
	0.5029
	0.5031
Total	2.5134
Mean :	= 2.5234/5 = 0.5027

Mean of the Data = 0.5027

c. Determine the standard deviation.

	X	(X-)	(X-)2
	0.5023	-0.0004	0.000000144
	0.5025	-0.0002	0.000000032
	0.5026	-0.0001	0.000000006
	0.5029	0.0002	0.000000048
	0.5031	0.0004	0.000000176
Total	2.5134		0.000000408
Mean :	0.5027

Standard deviation : s = 0.000319

d.

the range of molarities where you can be 95% confident that the true molarity lies for your sample i.e

95% confidence interval for population mean:

Formula for Confidence Interval for Population mean

Sample Mean : \overline{x}	0.5027
Sample Standard Deviation : s	0.000319
Sample Size : n	5
Degrees of freedom : n-1	4
Confidence Level :	95
	0.05
/2	0.025
t0.025,4	2.7764

95% confidence interval for population mean:

the range of molarities where you can be 95% confident that the true molarity lies for your sample : (0.5023,0.5031)