Question

A new thermometer is used to measure the body temperature of 100 healthy subjects. The mean and standard deviation for this sample are: X= 98.5F and s = 0.42F. Based on this information, test at a 0.05 significance level the hypothesis that the human body temperature is significantly different from 98.6F (i.e., test Ho: m = 98.6F versus H1: m ≠ 98.6F). Assume body temperatures normally distributed.

1. Can we reject the null hypothesis?

a) yes                b) no       

2. What is the P-value?

a) 0.027                        b) 0.0027             c)   0.0087              d) 0.087

3. Does the P-value support the result of the hypothesis testing?

a) Yes           b) No                        

An engineer claims to have found the way to improve the purity of gold after his refinement process. To prove is claim, 10 specimens of golden bars (1Kg each) are analyzed ‘before’ and ‘after’ the refinement process. The level of impurity is defined as mg of impurity content in 1 Kg of gold. Data are reported in the table below in terms of average impurity content per bar. Moreover, the mean and the standard deviation of the difference ‘before’ and after’ are found to be d = 0.7 mg/Kg and s_d = 1.15 mg/Kg. We want to test the claim of the engineer (use a 95% level of significance).

Specimen #	Impurity (mg/Kg) before	Impurity (mg/Kg) after
1	5.1	3.9
2	5.7	2.5
3	4.1	3.9
4	4.3	4.5
5	2.1	2.0
6	3.5	2.9
7	4.2	3.7
8	5.1	5.0
9	1.1	1.8
10	4.1	2.1

1. Which type of test is this?

a) test on paired proportions                   b) test on paired observation

c) test on paired variance                         d) test on difference of means

2. Should we believe the claim of the engineer (use 95% level of significance, one-sided and consider the P-value)?

a) Yes (P-value>0.05) b)No (P-value<0.05)   c)Yes (P-value<0.05) d)No (P-value>0.05)

Answer 1

The solution to this problem is given by