Claims about a Population Mean when σ is Known Objective: test a claim

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

 Critical Approach  Compare the test statistic to the critical value Left-tailedRight-tailed Two-tailed  P-Value Approach  Compare the p-value to α

1. Determine the null and alternative hypotheses 2. Select a level of significance 3. Compute the test statistic 4. Determine the critical value 5. Compare the critical value with the test statistic Reject the null hypothesis if the test statistic falls within the critical region!! 6. State the conclusion

 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

1. Determine the null and alternative hypotheses 2. Select a level of significance 3. Compute the test statistic 4. Determine the p-value 5. Compare the probability to α Reject the null hypothesis if the probability is less than the level of significance, α. 6. State the conclusion

 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

 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 , 12 together 13 – 17, 19, 20, 25, 26