In each exercise,
d. decide whether to reject or fail to...

Question

In each exercise,

d. decide whether to reject or fail to reject the null hypothesis, and

e. interpret the decision in the context of the original claim.

In Exercises 1 and 2, use the table, which lists the distribution of educational achievement for people in the United States ages 25 and older. It also lists the results of a random survey for two additional age groups. (Adapted from U.S. Census Bureau)

Table displaying educational attainment percentages for U.S. adults aged 25 and older, 30-34, and 65-69.

Use the data for 30- to 34-year-olds and 65- to 69-year-olds to test whether age and educational attainment are related. Use α=0.01.

Accepted Answer

All right, hello, everyone. So this question says, a nutritionist is testing whether the preference for salad type, Caesar, garden, or Greek is independent of gender, male or female. A random sample of 60 participants yields a test statistic of chi square equals 6.25. With degrees of freedom, DF equal to 2. At the 0.05 level of significance, decide whether to reject H not and interpret your decision in the context of the problem. So, first of all, what do we know? Right? In this case, we're testing whether salad preference is independent of gender. And in this case, we know that chi square is equal to 6.25. The degrees of freedom are equal to 2. In alpha, the significance level is 0.05. In this context, what is, or what are rather, the hypotheses? Well, the null hypothesis, that's H not, would state that salad preference is independent. Of gender Alternatively, the alternative hypothesis, that's H1 would state that salad preference is not independent of gender. Implying that they are related. So Because we already have the test statistic, we can go ahead and find the critical value. We use the chi square distribution table with DF equal to 2, and alpha equals 0.05. After referencing the chi square distribution, our critical chi square value. is equal to 5.991. Which now leads you to your decision, right? We have to compare the test statistic to the critical value. And we can see that our test statistic, that's 6.25, is greater than our critical value of 5.991. Because of this, Because the test statistic is greater than the critical value, we can reject the null hypothesis. So what does this mean? Right? We know that we can reject the null hypothesis. So how do we Describe this in the context of the problem. Well, Ultimately, there is sufficient evidence at the 0.05 confidence level to conclude that solid preference is related to gender. So essentially, men and women do differ in theirs solid preferences based on this sample. And now, this leads you to your final answer, which reads as follows. We reject H knot, meaning there is evidence that solid preference and gender are related. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

Key Concepts

Null Hypothesis

Significance Level (α)

Chi-Square Test

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