In Exercises 7–10, (c) explain whether the hypothesis test is left-tailed, right-tailed, or two-tailed.


An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.

Verified step by step guidance

1. Identify the null hypothesis (H₀) and the alternative hypothesis (Hₐ). The null hypothesis represents the claim to be tested, while the alternative hypothesis represents the claim the researcher wants to support. Here, H₀: μ ≥ 25 (the mean number of grams of carbohydrates is 25 or more) and Hₐ: μ < 25 (the mean number of grams of carbohydrates is less than 25).
2. Determine the direction of the inequality in the alternative hypothesis (Hₐ). Since the alternative hypothesis uses '<' (less than), this indicates a left-tailed test.
3. Understand the implications of a left-tailed test. In a left-tailed test, the critical region (where we would reject the null hypothesis) is located in the left tail of the sampling distribution.
4. Visualize the hypothesis test. Imagine a normal distribution curve with the critical region on the left side. This helps confirm that the test is left-tailed because we are testing for values significantly less than 25.
5. Conclude that the hypothesis test is left-tailed based on the structure of the alternative hypothesis and the direction of the inequality.

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1). The null hypothesis typically represents a statement of no effect or no difference, while the alternative hypothesis reflects the claim being tested. The outcome of the test determines whether to reject or fail to reject the null hypothesis.

One-Tailed vs. Two-Tailed Tests

In hypothesis testing, a one-tailed test evaluates the direction of the effect, either greater than or less than a certain value, while a two-tailed test assesses whether there is a significant difference in either direction. A left-tailed test is used when the alternative hypothesis states that a parameter is less than a certain value, whereas a right-tailed test is used when it states that the parameter is greater. Understanding the directionality is crucial for correctly interpreting the results.

Mean and Population Parameters

The mean is a measure of central tendency that represents the average of a set of values. In hypothesis testing, the population mean is often the parameter of interest, and claims about it are tested using sample data. In this context, the claim that the mean number of grams of carbohydrates in an energy bar is less than 25 grams indicates a specific population parameter that is being evaluated against the null hypothesis.