Question

(a) Biologists studying the healing of skin wounds measured the time taken for new cells to close a razor cut made in the skin of an anesthetized newt. Below are the data from 7 newts.

26, 25, 35, 34, 27, 31, 25

Find a 98% confidence interval for the mean healing time for all newts of this species.

(b) Which of the following statements is true regarding part (a)?

options for (b) (A) The population does not need to be normal. (B) The population must follow a t-distribution. (C) The population standard deviation σ must be known. (D) The population must be normal. (E) The population mean must be inside the confidence interval.

Answer 1

Solution:

x	x2
26	676
25	625
35	1225
34	1156
27	729
31	961
25	625
x=203	x2=5997

a ) The sample mean is

Mean = (x / n) )

=26+25+35+34+27+31+25 /7

=203/7

=29

Mean = 29

The sample standard is S

  S =( x² ) - (( x)² / n ) n -1

=5997-(203)²7 /6

=5997-5887/6

=110/6

=18.3333

=4.2817

The sample standard is4.28

Degrees of freedom = df = n - 1 = 7 - 1 =6

At 98% confidence level the t is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

t _/2,df = t_0.01,6 =3.143

Margin of error = E = t_/2,df * (s /n)

= 3.143 * (4.28/ 7)

= 5.08

Margin of error = 5.08

The 98% confidence interval estimate of the population mean is,

- E < < + E

29 - 5.08 < < 29 + 5.08

23.92 < < 34.08

(23.92, 34.08)

b ) Option b ) is correct

(B) The population must follow a t-distribution.