Question

The standard deviation of political tolerance (measured on a 10 point scale) in a sample of 27 adults is 3.6. The sample mean is 7.4. Test the null hypothesis that this sample is drawn from a population with a mean of 8.5 on the political tolerance measure (at α= .01).

Answer 1

Answer:

We can conclude that sample is drawn from a population with a mean of 8.5 on the political tolerance measure at α= .01 (accept the null hypothesis)

Step-by-step explanation:

$H_{0}$: mu=8.5

$H_{a}$: mu≠8.5

Test statistic can be calculated using the equation:

t=$\frac{X-M}{\frac{s}{\sqrt{N} } }$ where

• X  is the sample mean (7.4)

• M is the population mean on political tolerance (8.5)

• s is the standard deviation (3.6)

• N is the sample size (27)

Then t =$\frac{7.4-8.5}{\frac{3.6}{\sqrt{27} } }$  ≈−1.588

t-critical at  α= .01 and 26 degrees of freedom is 2.779

Since |t|=1.588 < 2.779, the result is not significant, we fail to reject the null hypothesis.