Question

we would like to conduct a hypothesis test at the 10% level of significance to determine whether the true mean score of all players in a bowling league differs from 150. the mean and standard deviation of the scores of 12 randomly selected players are calculated to be 162 and 17, respectively. Scores of all players in the league are known to follow a normal distribution. using critical value method, the decision rules to reject Ho if the value of the test statistic is:

a) less than -1.796 or greater than 1.796

b)less than -2.445 or greater than 2.445

c)less than -1.282 or greater than 1.282

d)less than -1.363 or greater than 1.363

e)less than -1.645 or greater than 1.645

Answer 1

Here hypothesis is ,

Two tailed test.

Rejection region :

Significance level = = 10% = 0.1 , /2 = 0.05

degrees of freedom = n - 1 = 12 - 1 = 11

Critical values for this two tailed test is ,

Left tail critical value =      { Using Excel, =T.INV(0.05,11 ) = -1.796 }

Right tailed critical value =    { Using Excel, =T.INV(1- 0.05,11 ) = 1.796 }

So, Rejection region = { t : t < -1.796 or t > 1.796 }

i.e. reject Ho if the value of the test statistic is less than -1.796 or greater than 1.796