Hello, can you pleasee explain to me how they got 0.475? Thats the only part tha

Question

Hello, can you pleasee explain to me how they got 0.475? Thats the only part that i dont get. th statistics and probability solutions manual complete business statistics Th edition chapter 7/problem 16 ete Business Statistics (7th Edition) Bookmark Show all steps: C ON pter 7, Problem 16 Problem An automobile manufacturer substitutes a different engine in cars that were known to have an average miles-per-gallon rating of 31.5 on the highway. The manufacturer wants to test whether the new engine changes the miles-per-gallon rating of the automobile model. A random sample of 100 trial runs gives 29.8 miles per gallon and 6.6 miles per gallon. Using the 0.05 level of significance, is the average miles-per-gallon rating on the highway for cars using the new engine different from the rating for cars using the old engine? Step-by-step solution Step 1 of 11 A Test at a .05 whether the new engines average 31.5 mpg. A random sample of n 00 yields a mean of T 29.8 and a standard deviation of s 6.6. 95 .02 29.8 30.21 hoceptance 1.96 1.96 Using the method of comparing R values: Hypotheses: Ho: H 31.5 H1: u 31.5

Explanation / Answer

a / 2 = 0.025

Total area of the standard normal curve is 1

So half area of standard normal curve is 0.5

The test is right tail test.

0.5 - 0.025 = 0.475

So the area next to the mean is 0.475, and z for 0.475 is 1.96.

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