Question

I am estimating that the population mean number of books read for pleasure in the last month is 1.5. My data set is as follows: 2 0 1 1 0 3 1 2 0 0 Please test this hypothesis at the .06 confidence level. provide the p value in the answer!

Answer 1

Sample size = n = 10

Sample mean = = 1

T

Standard deviation = s = 1.0541

Claim: The population mean number of books read for pleasure in the last month is 1.5.

The null and alternative hypothesis is

$H0:\mu=1.5$

$H1:\mu\neq 1.5$

Level of significance = 0.06

Here population standard deviation is unknown so we have to use t-test statistic.
Test statistic is

t Vn.

$t=\frac{1-1.5 }{\frac{1.0541}{\sqrt{10}}}=\frac{-0.5}{0.333333}=-1.5$

Degrees of freedom = n - 1 = 10 - 1 = 9

P-value = 2*P(T < - 1.5) = 0.1679

P-value > 0.06 we fail to reject null hypothesis.

Conclusion: The population mean number of books read for pleasure in the last month is 1.5.