Mathematics: A survey measures the motivation, attitudes, and study habits of freshman in college. Freshmans’ scores on this survey range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 110 and standard deviation σ = 20. You suspect that the next group of freshman will have a mean μ, which is different from 110 because they are often excited yet anxious about leaving college. To verify your suspicion, you test the hypotheses H0: μ = 110, Ha: μ ≠ 110 You give the survey to 50 high

x = 2.31662 x = −4.31662Step-by-step explanation:...

A survey measures the motivation, attitudes, and

Wintersavannah

20.01.2022

Option A) 0.0074

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 110

Sample mean, $\bar{x}$ = 20

Sample size, n = 100

Alpha, α = 0.05

Population standard deviation, σ = 115.35

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 110\\H_A: \mu \neq 110$

We use two-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{115.35 - 110}{\frac{20}{\sqrt{100}} } = 2.675$

Now, we calculate the p-value from the standard normal table.

P-value = 0.0074

Thus, the correct answer is

Option A) 0.0074

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