Question

Antonia read an article that said 26\%26%26, percent of Americans can speak more than one language. She was curious if this figure was higher in her city, so she tested H_0:p=0.26H
0
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:p=0.26H, start subscript, 0, end subscript, colon, p, equals, 0, point, 26 vs. H_\text{a}:p>0.26H
a
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:p>0.26H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 26, where ppp represents the proportion of people in her city that can speak more than one language.
Antonia took a sample of 120120120 people in her city found that 35\%35%35, percent of those sampled could speak more than one language. The test statistic for these results was z\approx 2.25z≈2.25z, approximately equals, 2, point, 25, and the corresponding P-value was approximately 0.010.010, point, 01. Assume that the conditions for inference were met.
Is there sufficient evidence at the \alpha=0.05α=0.05alpha, equals, 0, point, 05 level to conclude that the proportion of people in her city that can speak more than one language is greater than 26\%26%26, percent?

Answer 1

Considering that the p-value of the test is of less than 0.05, the correct option is:

A. Yes, because 0.01 < 0.05.

How the p-value influences the decision?

• If the p-value is less than the significance level, the null hypothesis is rejected.

• If the p-value is more than the significance level, the null hypothesis is not rejected.

In this problem, the p-value is of 0.01, which is greater than the significance level of 0.05, hence we reject the null hypothesis and we can conclude that the proportion of people in her city that can speak more than one language is greater than 26%, hence option a is correct.

More can be learned about p-values at brainly.com/question/26454209