Listed below are body temperatures of subjects measured at 8

Listed below are body temperatures of subjects measured at 8:00am and at 12:00am. Is the body temperature basically the same at both times using a 5% significance level?

            8:00am Temperatures: 97.0     96.2     97.6     96.4     97.8     99.2

            12:00am Temperatures:           98.0     98.6     98.8     98.0     98.6     97.6

Solution

The test of hypothesis is,

H0 : mu1 = mu2 Vs H1 : mu1 mu2

This is two sided test.

Here we use t-test because sample standard deviation is unknown ans sample size is small.

alpha = level of signficance = 0.05

Let X1 be the temperature measured at 8.00 am.

Let X2 be the temperature measured at 12.00 am

This we can done by using TI-83 calculator.

Assume variances are equal.

Steps :

Enter data in L1 and L2. STAT--> Enter --> enter data in L1 and L2.

STAT --> TESTS --> 4 : 2 - SampTTest --> Enter --> Data --> List1 : L1 --> List2 : L2 --> Freq1 : 1 --> Freq2 : 1 --> mu1 : mu2 --> Pooled : Yes --> Calculate

This will gives us following output.

t = -1.8465

df= 10

P-value = 0.09

P-value (0.09) > alpha

Accept H0 at 5% level of significance.

The body temperature basically the same at both times