10.2 HYPOTHESIS

TESTINGClaims about a Population Mean

when σ is Known

Objective: test a claim

CONDITIONS

To test a claim regarding the population mean assuming the population standard deviation is known,

1) A simple random sample is obtained

2) The population is normally distributed or the sample size is large

TWO APPROACHES Critical Approach

Compare the test statistic to the critical value

Left-tailed Right-tailed Two-tailed

P-Value Approach

Compare the p-value to α

STEPS TO TEST A CLAIM USING THE CLASSICAL APPROACH

1. Determine the null and alternative hypotheses

2. Select a level of significance3. Compute the test statistic

4. Determine the critical value5. Compare the critical value with the test

statisticReject the null hypothesis if the test statistic falls

within the critical region!!

6. State the conclusion

n

xz

00

SAMPLE An energy official claims that the oil

output per well in the US has declined from the 1998 level of 11.1 barrels per day. He randomly samples 50 wells throughout the US and determines the mean output to be 10.7 barrels per day. Assume that σ = 1.3 barrels. Test the researchers claim at the α = 0.05 level of significance.

Steps

STEPS TO TEST A CLAIM USING THE P-VALUE APPROACH

1. Determine the null and alternative hypotheses

2. Select a level of significance3. Compute the test statistic

4. Determine the p-value5. Compare the probability to α

Reject the null hypothesis if the probability is less than the level of significance, α.

6. State the conclusion

n

xz

00

SAMPLE An energy official claims that the oil

output per well in the US has declined from the 1998 level of 11.1 barrels per day. He randomly samples 50 wells throughout the US and determines the mean output to be 10.7 barrels per day. Assume that σ = 1.3 barrels. Test the researchers claim at the α = 0.05 level of significance.

Steps

TECHNOLOGY Z test

Enter either data or stats

Calculator will give the p-value

Compare the p-value to the level of significance

Reject the null hypothesis if the p-value < α

Assignment: page 527 11, 12 together 13 – 17, 19, 20, 25, 26