Testing Hypothesis on Population Mean

What is the first step in hypothesis testing?

• State the null hypothesis and the alternative hypothesis

• Selecting the significance level

• Drawing conclusions based on the data

• Conducting data analysis

Answer explanation

The first step in hypothesis testing is to state the null hypothesis and the alternative hypothesis, making it the correct choice.

Explain the concept of Type I error in hypothesis testing.

• Type I error is the correct rejection of a false null hypothesis.

• Type I error is the incorrect rejection of a true null hypothesis.

• Type I error is the incorrect acceptance of a true null hypothesis.

• Type I error is the correct acceptance of a false null hypothesis.

Answer explanation

Type I error is the incorrect rejection of a true null hypothesis.

What is the formula to calculate the test statistic for a population mean hypothesis test?

• (sample mean + population mean) / (sample standard deviation / sqrt(sample size))

• (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

• (sample mean - population mean) * (sample standard deviation / sqrt(sample size))

• (sample mean - population mean) / sample standard deviation

Answer explanation

The correct formula to calculate the test statistic for a population mean hypothesis test is (sample mean - population mean) / (sample standard deviation / sqrt(sample size)).

Explain the concept of Type II error in hypothesis testing.

• Type II error is the correct rejection of a false null hypothesis.

• Type II error is the incorrect rejection of a true null hypothesis.

• Type II error is the incorrect acceptance of a true null hypothesis.

• Type II error is the correct acceptance of a false null hypothesis.

Answer explanation

Type II error is the incorrect acceptance of a true null hypothesis, meaning failing to reject a false null hypothesis when it should have been rejected.

Explain the difference between a one-tailed and two-tailed hypothesis test.

• One-tailed tests are more accurate than two-tailed tests.

• Two-tailed tests are used for categorical data only.

• The difference between a one-tailed and two-tailed hypothesis test lies in the directionality of the alternative hypothesis.

• The difference is in the sample size required for each test.

Answer explanation

The difference between a one-tailed and two-tailed hypothesis test lies in the directionality of the alternative hypothesis.

The weight of the average 6th grade student's backpack (with books in it) is 18.4 lbs. The principal of the school thinks that the backpack does not weight 18.4 lbs. What is the null and alternate hypothesis? 

• H₀ = 18.4
  H_a = 18.4

• H₀ = 18.4
  H_a > 18.4

• H₀ = 18.4
  H_a < 18.4

• H₀ = 18.4
  H_a ≠ 18.4

Answer explanation

The correct choice is H0 = 18.4 and Ha ≠ 18.4, as the principal suspects the weight is different, not specifically greater or lesser.

Which of the following represents the appropriate null & alternative hypotheses?

The mean height of women is greater than 64"

• H₀: μ > 64"

  Hₐ: μ ≠ 64"

• H₀: μ < 64"

  Hₐ: μ > 64"

• H₀: p > 64"

  Hₐ: p ≠ 64"

• H₀: p = 64"

  Hₐ: p > 64"

Answer explanation

The correct choice is H₀: μ < 64" and Hₐ: μ > 64" because the null hypothesis states the mean height is less than 64" while the alternative hypothesis suggests it is greater than 64".

Which of the following is the basis in choosing between one-tailed test and two-tailed test?

• Null hypothesis

• Composite hypothesis

• Alternative hypothesis

• None of these

Answer explanation

The basis for choosing between one-tailed and two-tailed tests is the Alternative hypothesis.

For the 95% confidence level, what is the value for α?

• α = .01

• α = .05

• α = .10

• α = .025

Answer explanation

The correct value for α at a 95% confidence level is α = .05, which represents the significance level or the probability of making a Type I error in hypothesis testing.

The mean height of Grade 11 students is less than 66 inches. Determine if one tailed test or two-tailed test.

• One tailed test

• Two-tailed test

Answer explanation

The mean height being less than 66 inches indicates a one-tailed test, as we are only interested in one direction of the distribution.