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Test the claim that the mean GPA of night students is larger than 3.3 at the 0.10 significance level. The null and alternative hypothesis would be: H 0 : p ≥ 0.825 H 1 : p < 0.825 H 0 : μ ≤ 3.3 H 1 : μ > 3.3 H 0 : p ≤ 0.825 H 1 : p > 0.825 H 0 : μ ≥ 3.3 H 1 : μ < 3.3 H 0 : p = 0.825 H 1 : p ≠ 0.825 H 0 : μ = 3.3 H 1 : μ ≠ 3.3 Correct The test is: two-tailed right-tailed left-tailed Correct Based on a sample of 40 people, the sample mean GPA was 3.35 with a standard deviation of 0.03 The p-value is: Incorrect (to 2 decimals)

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Solution:-

- To test the claim that the mean GPA of night students is larger than 3.3 at the 0.10 significance level.

- The test asks for a single directional answer " larger " than a statistic value, this is a one way test. Hypothesis testing is about parameters, not statistics.

- The hypothesis would be:

           Null hypothesis: u ≥ 3.3

           Alternate hypothesis : u < 3.3

- The rejection region is defined by the Alternate Hypothesis (Ha) which is denoted by " u < 3.3 ". Hence, the rejection lies in the left tail. So a left tail test.              

- A sample size of, n = 40 people was taken.

- The sample mean, x_bar = 3.35

- The sample standard deviation, s = 0.03

- The significance level, (One-tail), α = 0.1

- We will perform a t-test for the given data, which is usually the case for one tailed tests.

         Degree of freedom df = n - 1 = 40 - 1 = 39

         α = 0.1 , one tail, df = 39, T-critical <  -2.392

- The t-value of the tests statistics can be calculated:

         [tex]t = \frac{ (u - x_b_a_r)*\sqrt{n} }{s} \\\\t = \frac{ (3.3 - 3.35)*\sqrt{40} }{0.03} \\\\t = - 10.54[/tex]

- Since the t-statistics = -10.54 below the t-critical value = -2.392; hence, falls into the rejection region. Thus, Null hypothesis is rejected.

- The corresponding p value is:

                        p < 0.00001

- The result is significant at p < 0.1

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