Question

A researcher is interested in whether or not body temps differ by time of day below is a table of temp data collected from 5 subjects determine if mean body temps are different at 8 am and 12 am with a 0.05 level of significance write hypothesis and draw bell curve Temps at 8 am: 98,97.6,97.2,97,98 Temps at 12am:97,98..8,97.6,97.7,98.8 Difference d: ??????????

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u_d = 0

Alternative hypothesis: u_d ≠ 0

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a matched-pairs t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard deviation of the differences (s), the standard error (SE) of the mean difference, the degrees of freedom (DF), and the t statistic test statistic (t).

s = sqrt [ (\sum (d_i - d)² / (n - 1) ]

s = 0.8438

SE = s / sqrt(n)

S.E = 0.37736

DF = n - 1 = 5 -1

D.F = 4

t = [ (x₁ - x₂) - D ] / SE

t = - 1.11

where d_i is the observed difference for pair i, d is mean difference between sample pairs, D is the hypothesized mean difference between population pairs, and n is the number of pairs.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 4 degrees of freedom is more extreme than -1.11; that is, less than - 1.11 or greater than 1.11.

Thus, the P-value = 0.329

Interpret results. Since the P-value (0.329) is greater than the significance level (0.05), we have to accept the null hypothesis.

Do not reject H0, the mean body temps are not different at 8 am and 12 am.