A researcher has constructed 80% confidence interval of µ = 45 ± 8, using a sample of *n *= 25 scores.

a. What would happen to the width of the interval if the researcher had used a larger sample size?

b. What would happen to the width of the interval if the researcher had used 90% confidence instead of 80%?

c. What would happen to the width of the interval if the sample variance increased? (Assume other factors constant.)

Problems 16 in chapter 9 described a study by Harlow (1959) in which infant monkeys were placed in cages with two artificial mothers. “One mother was made of wire mesh and had a bottle from which the infant could feed and the second mother of soft terry cloth but did not provide any food. Data for a sample of *n* = 9 monkeys showed that the infants spent an average an average of *M *= 15.3 hours per day with *SS* =216 with the terry cloth mother. Use the data to estimate how many hours per day would be spent with the terry cloth mother for the entire population of the infant monkeys. Make a point estimate and 80% confidence interval of the population mean.

There is some evidence suggesting that you likely to improve your test score if you rethink and change answers on a multiple –choice exam (Johnston, 1975). To examine this phenomenon, a teacher gave the same final exam to two sections of a psychology course. The students in one section were told to turn in their exams immediately after finishing, without changing any of the answers. In the other section, students were encouraged to reconsider each question and to change answers whenever they felt it was appropriate. The average score for the *n* = 20 students in the no- change section was *M* = 74.2 with SS = 460.6. The average for the *n *= 20 students in change section was M = 78.6 with *SS* = 512.2

a. Make a point estimate of the population mean difference mean difference between the test conditions.

b. Make a 95% confidence interval estimate of the mean difference between the two conditions.

c. Based on your answers to part b, would a two- tailed hypothesis test with α = .05 conclude that there is a significant difference between to conditions? (Is µ_{1 }-µ_{2 }= 0 an acceptable hypothesis?)

The following data were obtained in a study using three separate samples to compare three different treatments.

Treatments

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I II III

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4 3 8 *N* = 12

3 1 4 *G *= 48

5 3 6 *∑Χ ^{2}* = 238

4 1 6

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*M* = 4 *M* = 2 *M* = 6

*T* = 16 *T* = 8 *T* = 24

*SS * 2 *SS* = 4 *SS *= 8

a. Use an analysis of variance with α = .05 to determine whether there are significant difference among the treatments.

b. Compute the value for η^{2} for these data.

A researcher reports an F-ratio with *df* = 2, 24 for an independent –measures researcher study.

a. How many treatments conditions were compared in the study?

b. How many subjects participated in the entire study?

A developmental psychologist is examining the development of language skills from age 2 to age 5. Four different groups of children are obtained, one for each age with n = 15 children in each group. Each child is given a language skills assessments test. The resulting data were analyzed with an ANOVA to test to test for mean differences between age groups. The results of the ANOVA are presented in the following table. Fill in all missing values.

One possible explanation for why some birds migrate and others maintain year round residency in a singe location is intelligence. Specifically, birds with small brains, relative to their body size, are simply not smart enough to find food during the winter and must migrate to warmer climates where food is easily available (Sol, Lefebvre, & Rodriquez- Teijeiro, 2005). Birds with bigger brains, on the other hand, are more creative and can find food even when the weather turns harsh. Following are hypothetical data similar to actual research results. The numbers represent relative brain size for the individual birds in each sample.

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Non- Short Long
Migrating Distance Distance Migrants Migrant |

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18 6 4 *N* = 18

13 11 9 *G* = 180

19 7 5 *∑Χ ^{2}*= 2150

12 9 6

16 8 5

12 13 7

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*M* = 15 *M* = 9 *M *= 6

*T* = 90 *T* = 54 *T* = 36

*SS* = 48 *SS* = 34 *SS* = 16

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a. Use AVOVA with α =.05 to determine whether there are any significant mean differences among three groups of birds.

b. Compute η^{2, }the percentageof varianceexplained by the group difference, for these data.

- Use the turkey HSD posttest to determine which groups are significant different
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