Question

Given the Data set: 8.5, 8.7, 8.9, 8.2, 8.3, 8.4, 8.5 – Use this set for parts a to d. This is to be considered as set2 for part c

1. [Find the Mean, Mode, Median, Range, Midrange and Standard Deviation for the Data Set
2. Determine if the following data set has an outlier that can be disregarded
3. Using the given data set#2 from the given data and set #1 being (?⃐ = 8.7 , S = 0.47 and N = 7) determine if the two data sets are statistically the same or different using an 90% confidence interval.
4. Find the range for the sample mean value with 80% confidence interval. Make sure µ is isolated

Answer 1

[Find the Mean, Mode, Median, Range, Midrange and Standard Deviation for the Data Set

	x	x^2
1	8.2	67.24
2	8.3	68.89
3	8.4	70.56
4	8.5	72.25
5	8.5	72.25
6	8.7	75.69
7	8.9	79.21
total	59.5	506.09
Mean	8.5
SD	0.238
Mode	8.5	value with highest freq
Median	8.5	(N+1)/2 th value
Range	0.7	Max - min
Midrange	8.55	(min + max)/2
Lower Quartile(Q1)	8.3	(N+1)/4 th value
Upper quartile (Q3)	8.7	3(N+1)/2 th value
IQR	0.4	Q3 - Q1

Mean =

SD =

Determine if the following data set has an outlier that can be disregarded

Outlier is when a value lies outside the range (Q1 - 1.5IQR, Q3 + 1.5IQR)

Q1 - 1.5IQR = 7.7

Q3 + 1.5IQR = 9.3

since no values outside this range there are no outliers.

Using the given data set#2 from the given data and set #1 being (?⃐ = 8.7 , S = 0.47 and N = 7) determine if the two data sets are statistically the same or different using an 90% confidence interval.

Assuming the data comes from a normal population

We have

Null hyptohesis: The means are same for both sets

Alternative: The means are different

	1	2
n	7	7
mean	8.7	8.5
SD	0.47	0.238
Var	0.221	0.057

Pooled variance =

= 0.13878

Test Stat =

Level of significance (1 - 90% = 10%

Critical value at 10% =

= 1.7823 ......Using t-dist with df = 12 and p =0.025

then we substitute all the values

(-0.1549,0.5549)

Here since the null difference = 0 lies within the CI

We do not reject the null hypothesis thus concluding that at 10% level the means are significantly same.

Find the range for the sample mean value with 80% confidence interval. Make sure µ is isolated

Here since we do not have the population SD we will use a t-dist

80% confidence interval for population mean

Where the critical value at 20% (1-0.8)=

= 1.4398

Substituting the rest of values