Hypothesis testing examples on z test

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Hypothesis Testing Examples

Hypothesis Testing Examples

Test of Hypothesis Concerning normal population, infinite, Large Samples, with known population variance. ( Z Test)If the size of sample exceeds 30 it should beregarded as a large sample.Testing Hypothesis about population mean .

Z= x - S.E. of x

Z= x p/n x = sample mean p = population s.d. n= sample size Population size is infinite

.Some Hypothesis Testing ExamplesIllustration1 (two-tailed Test)The mean lifetime of a sample of 100 light tubes produced by a company is found to be 1,580 hours Test the hypothesis at 5% level of significance that the mean lifetime of the tubes produced by the company is 1,600 hours with standard deviation of 90 hours.


z= -2.22.Critical value of Z = 1.96Illustration2 One Tailed (Upper Tailed)

An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount will be maximum Rs180000. They are concerned that the true mean is actually higher than this, because they could potentially lose a lot of money. They randomly select 40 claims, and calculate a sample mean of Rs195000. Assuming that the standard deviation of claims is Rs50000 and set = .05, test to see if the insurance company should be concerned or not.


Step 1: Set the null and alternative hypothesesH0 : 180000H1 : > 180000

Step 2: Calculate the test statistic

z= = x /n= 1.897Step 3: Set Rejection Region

1.65Step 4: ConcludeWe can see that 1.897 > 1.65, thus our test statistic is in the rejection region. Therefore we fail to accept the null hypothesis. The insurance company should be concerned about their currentpolicies.

Illustration3 One Tailed (Lower Tailed)

Trying to encourage people to stop driving tocampus, the university claims that on average ittakes at least 30 minutes to find a parking space on campus. I dont think it takes so long to find a spot. In fact I have a sample of the last five times I droveto campus, and I calculated x = 20. Assuming thatthe time it takes to find a parking spot is normal,and that = 6 minutes, then perform a hypothesis test with level = 0.10 to see if my claim is correct.


Step 1: Set the null and alternative hypotheses

H0 : 30H1 : < 30

Step 2: Calculate the test statistic

Z= x /n = -3.727

Step 3: Set Rejection Region

Step 4: Conclude

We can see that -3.727