Question

520 52 461 5.2 459 476 4.99 474 456

just need answers outlined thanks

Answer 1

Since given that the data is normally distributed and the population SD is not given we use the t-dist to get the confidence interval.

	X	X^2
1	5.2	27.04
2	5.02	25.2004
3	4.61	21.2521
4	5.72	32.7184
5	4.59	21.0681
6	4.76	22.6576
7	4.99	24.9001
8	4.74	22.4676
9	4.56	20.7936
Total	44.19	218.0979
Mean	4.91
SD	0.375

Mean =

Σ. .. n

SD =

Σ (Στ)2 ✓Var η η –1

a) Point estimate is the sample mean.

Point estimate = 4.91

b)

(1- $1596226337353_blob.png$ )% is the confidence interval for population mean

SC (attn–1,0/27 n

$1596226337327_blob.png$ =1 - 0.95 = 0.05

Therefore the C.V. =

ta/2.n-1

=t_0.025,8

= 2.306   .............found using t-dist tables

Where Margin of error = C.v. * SE

=

SC tn-1,0/2 * n

Substituting the value

Ans: (4.6217, 5.1983)

Interpretation: we are 95% confident that the true mean lies within this interval

Option A

Option C is incorrect because it says sample pH and we look at the population.

Note: the data is only for 9 values so I have n = 9, but for the answers use n = 12 with all the values. If possible please uplod the rest of the values in comment section so that the answer can be correctly edited.

c)

$1596226337327_blob.png$ =1 - 0.99= 0.01

C.V. =

ta/2.n-1

=t_0.005,8

= 3.3554   .............found using t-dist tables

Substituting the value

Ans: (4.4906, 5.3294)

The confidence intervals are used to calculate a range of values for the unknown population parameter with some level of certainty. The basic equation of CI is

(1- $1596222023156_blob.png$ )% is the confidence interval for population parameter

(sample estimate - MOE, sample estimate + MOE)

Where MArgin of error = MOE = Std error * Critical value

The critical value is at $1596222023156_blob.png$  / 2,

Confidence level : c = (1- $1596222023156_blob.png$ )%

When the confidence level 'c' increases, we want to be more sure that the interval must contain the parameter. For this we would include more values so we do not miss the actual value in the interval. Incorporating more values increases the interval width.

The increase 'c' is associated with increased critical value. Since the critical value is used to calculate MOE, MOE increases with C.V.. Thus the width increases and in turn the confidence interval.

as the ....of the interval increases, This ....the Margin of error increases as well.