Question

Language Survey About 42.3% of Californians and 19.6% of all Americans over age five speak a language other than English at home. Using your class as the sample, conduct a hypothesis test to determine if the percent of the students at your school who speak a language other than English at home is different from 42.3%. sample means 38

22/38 speak another language

1. H₀: ___________
2. H_a: ___________
3. In words, define the random variable. __________ = _______________
4. The distribution to use for the test is ________________
5. Determine the test statistic using your data.
6. Draw a graph and label it appropriately. Shade the actual level of significance.
   1. Graph
   2. 1. Determine the p-value.
   3. Do you or do you not reject the null hypothesis? Why?
   4. Write a clear conclusion using a complete sentence.

Answer 1

The hypothesis being tested is:

H₀: p = 0.423

H_a: p ≠ 0.423

The random variable is the percent of the students at your school who speak a language other than English at home.

The distribution to use for the test is the z-distribution.

The graph is:

The test statistic, z = (p̂ - p)/√p(1-p)/n

z = (p̂ - 0.423)/√0.423(1-0.423)/38

z = 1.95

The p-value is 0.0517.

Since the p-value (0.0517) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the percent of the students at your school who speak a language other than English at home is different from 42.3%.

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