Question

A toothpick manufacturer wants every box to contain exactly (on average) 500 toothpicks. In a random sample of 25 boxes, mean is 498 toothpicks and standard deviation is 9 toothpicks.

Answer 1

One sample t-test.

$H_0:\mu=500.$

$H_a:\mu\ne500.$

Test statistic: $t=\frac{498-500}{\frac{9}{\sqrt{25}}}=-1.11.$

Degrees of freedom: $df=25-1=24.$

P-value: $p=2P(T<-1.11)=0.2780.$

Since the p-value is greater than 0.05, fail to reject the null hypothesis.

There is no sufficient evidence that the mean number of toothpicks is different of 500.