Statistics and Probability Unit Test

What is the standard form of a null hypothesis for a population proportion?

• p>0.5

• p=0.5

• p<0.5

• μ=0.5

Which of the following would be a valid alternative hypothesis for testing if a population proportion is greater than 0.3?

• p<0.3

• p=0.3

• p>0.3

• μ>0.3

In hypothesis testing for population proportion, which symbol represents the proportion in the null hypothesis?

• μ

• p

• x

• n

If you are testing whether a new product is preferred by more than 60% of customers, what is the null hypothesis?

• p=0.6

• p>0.6

• p≠0.6

• p<0.6

What is the alternative hypothesis for testing whether a population proportion is different from 50%?

• p=0.5

• p>0.5

• p<0.5

• p≠0.5

Which test statistic is commonly used for population proportion tests under the Central Limit Theorem?

• t-test

• z- test

• F- test

• Chi-square test

When the Central Limit Theorem is applied, the sampling distribution of the sample proportion is approximately:

• Skewed left

• Skewed right

• Normal

• Uniform

In which scenario is the z-test statistic appropriate for testing population proportions?

• Small sample sizes regardless of normality

• When the sample size is large and np and nq are both greater than 5

• Any situation where population parameters are unknown

• When the sample standard deviation is used instead of the population standard deviation

Which of the following best describes the Central Limit Theorem's role in hypothesis testing?

• It guarantees that all data is normally distributed

• It allows approximation of the sampling distribution as normal for large sample sizes

• It removes the need to calculate test statistics

• It ensures the rejection of the null hypothesis

What determines the boundaries of the rejection region for a hypothesis test?

• The sample proportion

• The significance level (α)

• The population mean

• The sample size