Question

Bottles of Langdon Falls water should contain, on average, 15 ounces of liquid— no more and no less. You select a sample of 36 bottles that has a mean of 14.915 ounces per bottle. Can you reject a null hypothesis that the population mean is equal to 15 ounces for the population of Langdon Falls bottles? Use a significance level of 5% and assume that the population standard deviation is 0.15 ounces. Please answer this question in three steps:

a) State the critical values you would use to make the decision

b) State the test statistic that you compute for this sample

c) State whether or not you would reject the null hypothesis

Answer 1

Sample size = 36

Sample mean = = 14.915

Population standard deviation = = 0.15

Level of significance = 5%

a) Since sample size is 36 ( greater than 30) and population standard deviation is given, we can use standard normal distribution for the sampling distribution of mean.

H₀: = 15

H_a: 15

Since, it's a two-sided hypothesis test, we would check for the values of (level of significance / 2) = 5%/2 = 2.5% or 0.025.

At this level of significance, using Z - table, critical values for 0.025 are -1.96 and 1.96

b) test statistic = ( - ) / SE(X)

where SE(X) is the standard error of , which is given by, SE(X) = /

So, test statistic = ( - ) /  (/)

= (14.915 - 15) / (0.15/6)

= -3.4

c) Since -3.4 is outside the range of -1.96 and 1.96, we would reject the null hypothesis.