Math Problem Statement

What’s the null and alternative hypotheses would be? What would be test statistic t = ?(3 decimal places) and what would be p-value = ? (4 decimal places) answer only; Women are recommended to consume 1800 calories per day. You suspect that the average calorie intake is different for women at your college. The data for the 11 women who participated in the study is shown below: 1850, 1695, 1973, 1847, 1930, 1921, 2105, 1619, 2047, 1973, 2041 Assuming that the distribution is normal, what can be concluded at the alpha = 0.1 level of significance?

Solution

Null hypothesis (H₀): μ = 1800
Alternative hypothesis (H₁): μ ≠ 1800

Test statistic (t) = 3.149
p-value = 0.0108

Since the p-value (0.0108) is less than the significance level (α = 0.1), we reject the null hypothesis. This suggests that the average calorie intake for women at your college is significantly different from 1800 calories per day.

Would you like more details or have any questions?

Here are 5 related questions:

  1. How is the test statistic for a t-test calculated?
  2. What assumptions are required for conducting a t-test?
  3. What does rejecting the null hypothesis imply in this context?
  4. How is the p-value interpreted in hypothesis testing?
  5. What happens if the significance level (alpha) is changed?

Tip: The p-value tells you the probability of observing the test results under the null hypothesis.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
t-Test
Significance Level
p-value

Formulas

t = (x̄ - μ) / (s / √n)

Theorems

Central Limit Theorem
Student's t-distribution

Suitable Grade Level

College Level