Significance Tests for Proportions

What is the parameter?

• p is the true proportion of elementary students who want a career helping others

• n is 128 children

• p is the mean number of children asked

• Fail to Reject the Ho

What is the null hypothesis

• H_o: p = .39

• H_o: p < .39

• H_o: p > .39

• H_o: p ≠ .39

What is the alternative hypothesis?

• H_o: p = .39

• H_o: p < .39

• H_o: p > .39

• H_o: p ≠ .39

Explain why the sample result gives some evidence to support the H_a: p > 0.39.

• because 317 children were asked

• because n(p) > 10

• because the sample proportion is higher than 0.39.

• because it was 3 years later.

When conducting a significance test for the difference in proportions, why do we pool the data when finding standard error?

• Because we like to swim

• Because we assume p1 = p2 in Ho

• Because the sample sizes are always equal

• To be safe and make sure we don't underestimate the standard error

• Because we don't the standard deviation.

What is our conclusion based on the sample proportion?

• There is evidence that more elementary students want a career helping others

• There is evidence that less elementary students want a career helping others

• There is not evidence of an increase in elementary students who want a career helping others

• There is is no way to conclude from the small sample

At a .05 significance level, what decision is made regarding the H_o?

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A Gallup poll report revealed that 72% of teens said they rarely or never argue with their friends. Yvonne wonders if this result is true for her school. She surveys a random sample of 150 students and 64% of them say they rarely or never argue with friends. She uses the data to perform a test of Ho: p = 0.72 versus Ha: p=/= 0.72. The test yields a p-value of 0.0291. What conclusion would you make for a significance level of 5%?

• Since our p-value of 0.0291 is more than 5%. we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

• Since our p-value of 0.0291 is less than 5%. we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

• Since our p-value of 0.0291 is more than 5%. we reject the null hypothesis. We have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

• Since our p-value of 0.0291 is less than 5%. we reject the null hypothesis. We have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

Whatever probability we choose as the cutoff for what is small is what we call the ____________________.

• importance level

• significance level

• meaningfulness level

• insightfulness level

Lumber companies dry freshly cut wood in kilns before selling it. A certain percentage of boards develop cracks on their ends during drying. The current drying procedure is known to produce cracks in 16% of boards. The drying supervisor wants to try a new method that she believes will result in a proportion of cracked boards that is less than 16%. Write the appropriate hypotheses.

• Ho: p = 0.16

  Ha: p = 0.16

• Ho: p = 0.16

  Ha: p =/= 0.16

• Ho: p = 0.16

  Ha: p > 0.16

• Ho: p = 0.16

  Ha: p < 0.16