MS 150 Statistics q09: Hypothesis Testing • Name:

In SC 130 Physical Science laboratory ten KG gathered the above data on the apparent optical depth of a coin in water. The third column is index of refraction of water values for each measurement. For the data in the third column:

• sample size n = 6
• sample mean x = 1.51
• sample standard deviation sx = 0.43

Theoretically the index of refraction for water is 1.33. Use a hypothesis test to determine whether KG's data supports a theoretic value of 1.33 (fails to reject the null hypothesis) or disconfirms a theoretic value of 1.33 (rejects the null hypothesis).

Given the following hypothesis:
Null hypothesis: H₀: μ = 1.33
Alternate hypothesis: H₁: μ ≠ 1.33
Use α = 0.05

1. SE = ____________________ Calculate the standard error of the sample mean x.
2. df = ___________ Determine the degrees of freedom.
3. t_c = ____________________ Calculate the value of t_critical
4. t = ____________________ Calculate the t-statistic t.
5. ________________________________________ Would we reject the null hypothesis or fail to reject the null hypothesis at α = 0.05?
6. __________ Does KG's data support or disconfirm the theoretic index of refraction of 1.33 water?