Having been rejected from the Boomers, Ralph is still in search of a bowling tea

Question

Having been rejected from the Boomers, Ralph is still in search of a bowling team. He tries out for the Strikers. You are the team statistician for the Strikers and are skeptical when Ralph tells you that he bowls an average of 185, and set up a tryout.

After bowling 36 games, Ralph has averaged 174.68 with a standard deviation of 25. Calculate the appropriate test statistic (z or t) for this sample average.

What is the P-Value of this test statistic? Why is the answer 0.025? What table do I use and how do I look it up? P(t<2.064)

Explanation / Answer

Here, x = 174.68 , mean =185 , s = 25 , n = 35

By normal distribution formula,

t = ( x - mean) / (s/sqrt(n))

= ( 174.68 - 185) / ( 25 / sqrt(36))

= -2.48

Now, we need to find p value using t = -2.48 , df = 36-1 = 35

p value = 0.018 for two tail with 0.05 significance level

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