Understanding Hypothesis Testing

Fay investigates if the proportion of bilingual individuals in her city exceeds the national average of 26%. She samples 120 people, finding 33% are bilingual. Using a Z statistic of 1.83, she calculates the P-value to determine if this result is statistically significant. If the P-value is below her significance level, she rejects the null hypothesis, suggesting a higher bilingual rate in her city.

What was Fay curious about after reading the article?

• If fewer people in her city can speak multiple languages compared to the national average.

• If more people in her city can speak multiple languages compared to the national average.

• If the article was published in a reputable journal.

• If the national average of multilingual speakers is accurate.

What was the sample size Fay used for her study?

• 150

• 120

• 200

• 100

How did Fay calculate the sample proportion of multilingual speakers?

• By using the national average directly.

• By estimating based on a survey.

• By dividing the number of multilingual speakers by the sample size.

• By dividing the number of multilingual speakers by the total population of the city.

What does the Z statistic represent in Fay's analysis?

• The probability of the null hypothesis being true.

• The number of standard deviations the sample proportion is from the assumed population proportion.

• The difference between the sample mean and the population mean.

• The total number of people surveyed.

What is the assumed population proportion Fay used in her calculations?

• 0.50

• 0.40

• 0.26

• 0.33

What does a P-value indicate in hypothesis testing?

• The probability of the null hypothesis being true.

• The probability of the alternative hypothesis being true.

• The probability of the sample size being sufficient.

• The probability of observing the sample result if the null hypothesis is true.

What is the significance level used for in hypothesis testing?

• To determine the sample size.

• To find the mean of the sample.

• To calculate the Z statistic.

• To decide whether to accept or reject the null hypothesis.

If the P-value is lower than the significance level, what should be done?

• Recalculate the Z statistic.

• Accept the null hypothesis.

• Reject the null hypothesis.

• Increase the sample size.

What would Fay conclude if her significance level was 5% and the P-value was 3%?

• Reject the null hypothesis.

• Decrease the sample size.

• Increase the significance level.

• Fail to reject the null hypothesis.

What happens if the significance level is set lower than the P-value?

• The sample size is increased.

• The null hypothesis is not rejected.

• The null hypothesis is accepted.

• The null hypothesis is rejected.