# Hypothesis testing problems

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1. In a population of typical college students, µ=75 on a statistics final exam (σx=6.4). For 25 students who studied statistics using a new technique, X=72.1. Using two tails of the sampling distribution and the .05 criterion: A.) what is the critical value? B.) Is this sample in the region of rejection? How do you know? C.) Should we conclude that the sample represents the population of typical students? D.) Why?

2. On a standard test of motor coordination, a sports psychologist found that the population of average bowlers had a mean score of 24, with a standard deviation of 6. She tested a random sample of 30 bowlers at Fred's Bowling Alley and found a sample mean of 26. A second random sample of 30 bowlers at Ethel's Bowling Alley had a mean of 18. Using the criterion of ρ= .05 and both tails of the sampling distribution, what should she conclude about each sample's representativeness of the population of average bowlers?

3.) Foofy computes the X(sample mean of Xs, can't figure out how to make the line above the X) from the data that her professor says is a random sample from population Q. She correctly computes that this mean has a z-score of +41 on the sampling distribution fro population Q. Foofy claims she has proven that this could not be a random sample from population Q. Do you agree of disagree? Why?

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Step by step method for computing test statistic for comparing mean is given in the answers

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1. In a population of typical college students, µ=75 on a statistics final exam (σx=6.4). For 25 students who studied statistics using a new technique, X=72.1. Using two tails of the sampling distribution and the .05 criterion: A.) what is the critical value? B.) Is this sample in the region of rejection? How do you know? C.) Should we conclude that the sample represents the population of typical students? D.) Why?

Answer

H0: Mean = 75

H1: Mean ≠ 75

Test Statistic used

Significance level = 0.05

Decision rule : Reject the null hypothesis if the calculated value of test statistic is greater than the critical value .

Details

Z Test of Hypothesis for the Mean

Data

Null Hypothesis = 75

Level of Significance 0.05

Population Standard Deviation 6.4

Sample Size 25

Sample Mean 72.1

Intermediate Calculations

Standard Error of the Mean 1.28

Z Test Statistic -2.265625

Two-Tail Test

Lower Critical Value -1.959963985

Upper Critical Value 1.959963985

p-Value 0.023474353

Reject the null hypothesis

A.) What is the critical value?

Critical value = 1.9599

B.) Is this sample in the region of rejection? ...

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