7/30/2019 Yarensky Homework #9

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Kevin Fisher 

May 4, 2012

Psychology Statistics – Yarensky 05

Homework #9

1.  Dr. Sweet would use a directional hypothesis because he is predicting an improvement in grades, not just a generalchange. The direction (increased scores, improvement) is specified and clear.

2. H0; µ ≥ 81.4 – Chocolate had no effect on (or decreased) exam scores.H0; µ > 81.4 – Chocolate improved exam scores.

3.  He can say that chocolate does produce a significant improvement in exam scores, but only if alternative explanations

to the increase can be ruled out4. 

a. i.  H0 is true and you fail to reject it – correct decision

ii.  H0 is true and you reject it – false positive, Type I error 

iii.  H0 is false and you fail to reject it – false negative, Type II error iv.  H0 is false and you reject it – correct decision

 b.  Yes, it could be that chocolate has no effect, but due to the sampling error, his class scored better than usual.

c.   No – false negatives (type II errors) can only occur when you fail to reject the null hypothesis.5. 

a.  The probably of a false positive is called α. This is the level of significance. It is determined by the level of significance chosen by the experimenter. The level of significance is the probability of making a Type I error.It is the probability that we will conclude that an effect exists when in fact there is none

 b.  The probability of correctly rejecting the null hypothesis is called the power of a statistical test, and it isdesirable that power be high. It is powerful to the extent that it correctly identifies situations where thealternative hypothesis is true (where the null hypothesis is false).

c.  β is the probability of a false negative (Type II error). Power is 1-beta, where beta is the probability of a Type

II error, failing to reject a false null hypothesis. In a hypothesis test, the acceptable probability of a Type IIerror; 1−β is called the power of the test. As power goes up, β goes down.

6.  Test statistic = sample statistic – population parameter Standard error of sample statistic

7.  The four staged of hypothesis testing are:a.  State the null and alternative hypothesis

 b.  Set the criterion for rejecting the null hypothesisc.  Collect data from a sample and compute the observed values of the sample statistic of interest and the test

statisticd.  Interpret your results.

8. a.  The standard deviation of this population distribution tells us that if we had a bunch of ice cream cones made

up, the average difference between each cone’s weight and the mean (X - µ) would be approximately 1.3 oz. b.  Use a z-distribution: z = (X- µ)/ σ (9-8.4)/1.3 = .46 z=.46 p = 32.28%

9. a.  You are using a sampling distribution. 1.3/√25

 b.  If we took many samples of 25 cones, the average deviation of the sample means from the population meanswould be about 0.26 ounces.

c. d.  Before, we were looking at deviations of individuals from the population mean –  in the previous, we’re

looking at deviations of sample means from the population mean. As the entire sample should represent the population between than a single individual, we’d expect the probability to be lower in the more recentexample.