Using Minitab Chapter 8: Hypothesis Testing - One Sample

Each chapter has its own page of screenshots.

• Chapter 8.2 - Hypothesis Tests About a Proportion 2 Here we use Minitab like a calculator. All we need is the number of successes (x) and the number of trials (n). Minitab returns the test statistic (zpˆ) and the P -value. It also gives you a conﬁdence interval for the population proportion (p).

• Chapter 8.3 - Hypothesis Tests About a Mean: σ Not Known (t-test)

– Using Summarized Data 3 Here we use Minitab like a calculator. All we need is the sample size (n), sample mean (¯x), and sample standard deviation (s). Minitab returns the test statistic (tx¯) and the P -value. It also gives you a conﬁdence interval for the population mean (µ).

– Using Sample Data 4 Here, Minitab takes sample data and a hypothesized value for the population mean to conduct a hypothesis test. It returns some summary statistics from the sample, the test statistic tx¯, and the P -value based on the alternate hypothesis.

• Chapter 8.4 - Hypothesis Tests About a Mean: σ Known 5 Here we use Minitab like a calculator. All we need is the sample size (n), the sample mean (¯x), and the population standard deviation (σ). If you don’t have the population standard deviation (and you usually won’t) use one of the methods described in Chapter 8.3. 2

Chapter 8.2 - Hypothesis Tests About a Proportion Here we use Minitab like a calculator. All we need is the number of successes (x) and the number of trials (n). Minitab returns the test statistic (zpˆ) and the P -value. It also gives you a conﬁdence interval for the population proportion (p). We’ll demonstrate Example 1 from Chapter 8.2. Suppose you ﬂip a coin 100 times and get 43 heads. Test the claim that the coin is not fair.

n = 100, x = 43,p ˆ = .43, H0 : p = 0.50 H1 : p 6= 0.50

Based on the normal approximation, the test statistic zpˆ = −1.40 and the P -value is 0.162. Fail to reject H0. * The other option is Exact. This would produce a better P -value based on the binomial distribution. However, if you want your answers to match those in the book you should use Normal Approximation. The diﬀerence should not be that great. 3

Chapter 8.3 - Hypothesis Tests About a Mean: σ Not Known Using Summarized Data: Here we use Minitab like a calculator. All we need is the sample size (n), sample mean (¯x), and sample standard deviation (s). Minitab returns the test statistic (tx¯) and the P -value. It also gives you a conﬁdence interval for the population mean (µ). Here is the Example from Chapter 8.3.

n = 40,x ¯ = 9.8, s = 1.7, H0 : µ = 10.3 H1 : µ 6= 10.3

The test statistic tx¯ = −1.86 and the P -value is 0.070. Fail to reject H0. 4

Chapter 8.3 - Hypothesis Tests About a Mean: σ Not Known Using Sample Data: Here, Minitab takes sample data and a hypothesized value for the population mean to conduct a hypothesis test. It returns some summary statistics from the sample, the test statistic tx¯, and the P -value based on the alternate hypothesis. Example: The cholesterol levels from a sample of 10 overweight men is contained in a ﬁle called Cholesterol Data.MTW. Test the claim that the population mean for all overweight men is greater than 170 mg/DL.

The test statistic tx¯ = 2.17 and the P -value is 0.029. You may or may not reject H0 depending on your signiﬁcance level. 5

Chapter 8.4 - Hypothesis Tests About a Mean: σ Known Here we use Minitab like a calculator. All we need is the sample size (n), the sample mean (¯x), and the population standard deviation (σ). If you don’t have the population standard deviation (and you usually won’t) use the method described in Chapter 8.3. Here is the Example from Chapter 8.4.

n = 63,x ¯ = 55.12, σ = 1.7, H0 : µ = 55.90 H1 : µ < 55.90

The test statistic zx¯ = −3.64 and the P -value is 0.000 (rounded to 3 decimal places). Reject H0.