The average population weight of residents of Harrisonburg is [tex]195 \pm 25[/tex] pounds ([tex]\mu \pm \sigma[/tex]) in a normally distributed distribution. Suppose we select a sample of 400 children ([tex]n = 400[/tex]) residents and wish to test if their average weight of 188 pounds is significantly smaller than that of the population. List and explain the 5 steps of hypothesis testing. What conclusion do you arrive at?

The five steps of hypothesis testing including formulating hypothesis, determining the level of significance, calculating the test statistic, computing the p-value, and making a conclusion are applied in the problem. Subsequently, the difference between average weights of children and the population is statistically tested.

Explanation:

The five steps of hypothesis testing in this case are as below:

Formulating the Hypotheses: In this situation, the null hypothesis H0: μ = 195 (the average weight of children = population average) and the alternative hypothesis H1: μ < 195 (the average weight of children is less than the population average).
Significance Level: Determine the level of significance, typically 5% or α = 0.05 in most cases.
Statistical Analysis: Compute the test statistic. Here, the test statistic = (X - μ)/(σ/√n) where X is sample mean (188), μ is the population mean (195), σ is the standard deviation (25), and n is the sample size (400). This statistic will follow the normal distribution.
P-Value : Calculate the probability of getting a test statistic as extreme as what was observed (known as the p-value).
Conclusion: If p-value is less than α, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

In the end, depending on the p-value, we can arrive at a conclusion whether the average weight of children is significantly smaller than that of the population or not.

Learn more about Hypothesis Testing here:

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