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Answer :
Final answer:
The alternative hypothesis is that the population mean is less than 108.5 grams of protein per day. The p-value is a measure of the strength of evidence against the null hypothesis. Based on the given data and p-value, we can determine whether the null hypothesis proves the given statement or lacks evidence.
Explanation:
In hypothesis testing, we start with a null hypothesis (H0) and an alternative hypothesis (Ha). The null hypothesis states that the population mean (µ) is greater than or equal to 108.5 grams of protein per day. The alternative hypothesis states that the population mean is less than 108.5 grams of protein per day.
Based on the given data, we have a sample size of 42, a sample mean of 122.35, and a standard deviation of 25.095. To determine the alternative hypothesis and p-value, we need to perform a hypothesis test.
Since we have a sample size greater than 30 and the population standard deviation is unknown, we can use a t-test. Using the t-test, we calculate the t-value and compare it to the critical t-value at a given significance level (usually 0.05).
After performing the calculations, we find that the alternative hypothesis is Ha: µ < 108.5 and the p-value is the probability of observing a sample mean of 122.35 or less, given that the null hypothesis is true.
Based on the p-value, if it is less than the significance level (0.05), we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the alternative hypothesis.
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