In Exercises 1–10, use the following weights (g) of Hershey’s Kisses from Data Set 38 “Candies” in Appendix B.

Sign Test Repeat Exercise 3 using the sign test to test the claim that the sample of weights is from a population with a median of 4.5333 g.

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Step 1: Understand the sign test. The sign test is a non-parametric test used to determine whether the median of a sample differs from a specified value. It involves comparing each data point to the hypothesized median and recording whether the data point is above, below, or equal to the median.

Step 2: Compare each weight in the sample to the hypothesized median of 4.5333 g. For each weight, determine whether it is greater than, less than, or equal to the median. Record the signs (+ for greater, - for less, and 0 for equal).

Step 3: Count the number of positive signs (+), negative signs (-), and zeros (0). The zeros are excluded from the test, as they do not contribute to the comparison.

Step 4: Use the binomial distribution to calculate the probability of observing the given number of positive or negative signs under the null hypothesis that the population median is 4.5333 g. The null hypothesis assumes that the weights are equally likely to be above or below the median.

Step 5: Compare the calculated probability (p-value) to the significance level (e.g., 0.05). If the p-value is less than the significance level, reject the null hypothesis and conclude that the sample median differs from 4.5333 g. Otherwise, fail to reject the null hypothesis.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Sign Test

The sign test is a non-parametric statistical method used to determine if there is a significant difference between the median of a sample and a specified value. It involves comparing each observation to the hypothesized median and counting the number of positive and negative differences. This test is particularly useful when the sample size is small or when the data does not meet the assumptions required for parametric tests.

Median

The median is a measure of central tendency that represents the middle value of a dataset when it is ordered from least to greatest. In cases where the dataset has an even number of observations, the median is calculated as the average of the two middle values. The median is less affected by outliers and skewed data compared to the mean, making it a robust measure for understanding the typical value in a dataset.

Hypothesis Testing

Hypothesis testing is a statistical procedure used to make inferences about a population based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample data to determine whether to reject the null hypothesis. The outcome is assessed using a significance level, which indicates the probability of making a Type I error, or incorrectly rejecting the null hypothesis when it is true.

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