Question

Data set :

Data Set G: Assume the population values are normally distributed.

Random variable: x = weight of border collie in pounds

sample size = 25

34.1

40.8

36.0

34.9

35.6

43.4

35.4

29.3

33.3

37.8

35.8

37.4

39.0

38.6

33.9

36.5

37.2

37.6

37.3

37.7

34.9

33.2

36.2

33.5

36.9

1. Choose another confidence level similar to one found in the homework (do not use the
confidence level from the posted example). Based on the second confidence level, find the
critical value and calculate the margin of error. In a table, state the second confidence level,
the point estimate, the critical value, margin of error, and confidence interval. Put the proper
symbols in the left column and the value of the statistic or properly formatted confidence
interval in the right column. The statistics and confidence interval should be rounded properly.
Label this “Table 5: Confidence Interval 2.”

Answer 1

Solution:

Here, we have to find the confidence interval for the population mean. We have to use the confidence level other than that of default confidence level 95%, so we assume 98% confidence level for this interval. Confidence interval formula is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = Xbar ± Margin of error = Xbar ± E

Where, t is critical value, Xbar is sample mean, S is sample standard deviation and n is sample size.

From given sample data, we have

Point Estimate = Sample mean = Xbar = 36.252

Sample standard deviation = S = 2.76979542

Sample size = n = 25

Degrees of freedom = n – 1 = 25 – 1 = 24

Confidence level = 98%

Critical t value = 2.4922

(by using t-table)

Standard error = S/sqrt(n) = 2.76979542/sqrt(25)

Standard error = 0.553959084

Margin of error = t*S/sqrt(n) = critical value * standard error

Margin of error = 2.4922*0.553959084

Margin of error = E = 1.3806

Confidence interval = Xbar ± E

Confidence interval = 36.252 ± 1.3806

Lower limit = 36.252 - 1.3806 = 34.87

Upper limit = 36.252 + 1.3806 = 37.63

Confidence level = (34.87, 37.63)

We are 98% confident that the population mean will lies between 34.87 and 37.63.

Now, let us consider 99% confidence level.

Xbar = 36.252, S = 2.76979542,

Standard error = 0.553959084,

n = 25, df = 24

Critical t value = 2.7969

(by using t-table)

Margin of error = E = 2.7969*0.553959084 = 1.5494

Lower limit = 36.252 - 1.5494 = 34.70

Upper limit = 36.252 + 1.5494 = 37.80

Confidence interval = (34.70, 37.80)

We are 99% confident that the population mean will lies between 34.70 and 37.80.