# Chapter 9b One-Tailed Test about a Population Mean: Small-Sample Case (n < 30)One-Tailed Test about a Population Mean: Small-Sample Case (n < 30) Tests.

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Chapter 9b One-Tailed Test about a Population Mean: Small-Sample Case (n < 30)One-Tailed Test about a Population Mean: Small-Sample Case (n < 30) Tests about a Population ProportionTests about a Population Proportion

Using the p  Value Using the p  Value 4. Compute the value of the test statistic. 5. Compute the p –value. 6. Determine whether to reject H 0. Because p –value =.0021 <  =.05, we reject H 0. One-Tailed Test about a Population Mean: Small-Sample Case ( n < 30) The p -value computed by Excel is.0021

n > 30 ? s known ? Popul. approx.normal ? s known ? Use s to estimate s Use s to estimate s Increase n to > 30 Yes Yes Yes Yes No No No No Summary of Test Statistics to be Used in a Hypothesis Test about a Population Mean

n The equality part of the hypotheses always appears in the null hypothesis. in the null hypothesis. In general, a hypothesis test about the value of a In general, a hypothesis test about the value of a population proportion p must take one of the population proportion p must take one of the following three forms (where p 0 is the hypothesized following three forms (where p 0 is the hypothesized value of the population proportion). value of the population proportion). A Summary of Forms for Null and Alternative Hypotheses about a Population Proportion One-tailed (lower tail) One-tailed (upper tail) Two-tailed

Test Statistic Tests about a Population Proportion where:

n Rejection Rule H 0 : p  p  Reject H 0 if z > z  Reject H 0 if z < -z  Reject H 0 if |z| > z  H 0 : p  p  H 0 : p  p  Tests about a Population Proportion

Example: NSC Two-Tailed Test about a Population Proportion For a Christmas and New Year’s week, the National Safety Council estimated that 500 people would be killed and 25,000 injured on the nation’s roads. The NSC claimed that 50% of the accidents would be caused by drunk driving.

Example: NSC n Two-Tailed Test about a Population Proportion A sample of 120 accidents showed that 67 were caused by drunk driving. Use these data to test the NSC’s claim with  = 0.05.

Two-Tailed Test about a Population Proportion 1. Determine the hypotheses. 2. Specify the level of significance. 3. Select the test statistic.  =.05 4. State the rejection rule. Reject H 0 if | z |> 1.96 Using the Test Statistic Using the Test Statistic (two-tailed test)

Two-Tailed Test about a Population Proportion Using the Test Statistic Using the Test Statistic 5. Compute the value of the test statistic. a common error is to use in this formula

Two-Tailed Test about a Population Proportion Using the Test Statistic Using the Test Statistic 6. Determine whether to reject H 0. Because 1.278 > -1.96 and -1.96 and < 1.96, we cannot reject H 0.

n Formula Worksheet Using Excel to Conduct Hypothesis Using Excel to Conduct Hypothesis Tests about a Population Proportion Note: Rows 14-121 are not shown.

Using Excel to Conduct Hypothesis Using Excel to Conduct Hypothesis Tests about a Population Proportion n Value Worksheet Note: Rows 14-121 are not shown.

Using the p  Value Using the p  Value 4. Compute the value of the test statistic. 5. Compute the p –value. 6. Determine whether to reject H 0. Because p –value =.201 >  =.05, we cannot reject H 0. The p -value computed by Excel is.201 Two-Tailed Test about a Population Proportion

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