Question

a neuologist measured he brain mass of 22 balloons and recorded the following results in grams, 131 140 126 133 109 1113 140 146 123 147 142 142 122 141 111 102 127 139 142 129 132. at a 0.05 significance level, est the claim that the average brain mass of baboons is equal to 128.1 grams. assum the population is normaly distributedd.

hypothesis:

test stats:

p value

sketch graph

result

conclusion

Answer 1

Solution:-

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

Null hypothesis: u= 128.1
Alternative hypothesis: u 128.1

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

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

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

SE = s / sqrt(n)

S.E = 2.85336

DF = n - 1

D.F = 21
t = (x - u) / SE

t = - 0.475

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 21 degrees of freedom is less than -0.475 or greater than 0.475

Thus, the P-value = 0.64

Interpret results. Since the P-value (0.64) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that the average brain mass of baboons is equal to 128.1 grams.