Question

Bottles of Langdon Falls water should contain, on average, 1600 ounces of liquid— no more and no less. You select a sample of 52 bottles that has a mean of 1595.91 ounces per bottle. Assume that the population standard deviation is known to be 10 ounces. Can you reject a null hypothesis that the population mean is 1600 ounces for the population of Langdon Falls bottles? Use a significance level of 1%.

Please state the critical values you would use to make the decision.

  

Please state the test statistic that you compute for this sample.

Please state the p-value that you compute for this sample.

Please state whether or not you would reject the null hypothesis.

Answer 1

Solution:

Given ,

= 1600

claim : = 1600 or not

n = 52

= 1595.91

= 10

Use = 1% = 0.01

/2 = 0.005

Hypothesis are

H0 : = 1600 (null hypo.)

H1 :     1600

Now , observe that ,there is   sign in H1. So , the test is two tailed.

So there are two critical values.   i.e.  

i.e.   2.576 (Use z table to find this value)

Critical values are -2.576 and 2.576

The test statistic z is given by

z =

= (1595.91 - 1600) / (10/52)

= -2.95

Since |z| = 2.95 is greater  than |2.576| , we reject the null hypothesis.

For two tailed test :

p value = 2 * P(Z < -z)

= 2 * P(Z < -2.95)

= 2 * 0.0016

= 0.0032

Since the p value is less than = 0.01 , we reject the null hypothesis.

Since |z| = 2.95 is greater  than |2.576| , we reject the null hypothesis