Answer :
Final answer:
The p-value calculated from a one-sample t-test is approximately 0.008. This indicates that the mean weight of 20-year-old vegetarian women is significantly less than that of all 20-year-old women.
Explanation:
The subject of your question is hypothesis testing, specifically involving a one sample t-test. The null hypothesis in this scenario is that the mean weight of vegetarian women is equal to the population mean of all 20-year old women, which is 128 pounds. The alternative hypothesis is that the mean weight of vegetarian women is less than the population mean.
To calculate the t-value, you subtract the population mean from the sample mean, divide the result by the standard deviation, and then divide this by the square root of the sample size:
(122 - 128)/(15/√28). This calculation yields a t-value approximately equal to -2.65.
If we look up this t-value in a t-distribution table (with 27 degrees of freedom, which is the sample size minus 1), the p-value is between 0.01 and 0.005. Hence, the p-value is approximately 0.008. Because the p-value is less than 0.05, we reject the null hypothesis. This shows that the mean weight of 20-year-old vegetarian women is significantly less than the mean weight of all 20-year-old women.
Learn more about Hypothesis Testing here:
https://brainly.com/question/34171008
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