The next several problems require that you calculate 95% confidence intervals for the value of a population parameter or conduct null/alternative hypothesis tests with one of the hypothesis testing procedure.

Two-way ANOVASesame Street revisited.

Throughout the 1970s, Sesame Street became a very popular program for children, and it remains popular to this day. There were, however, a number of social science researchers (including sociologists) who doubted that all the impacts of the program were desirable impacts. The goals of the program were to not only enhance school readiness among kindergarten-age children, but to reduce or eliminate the readiness gap that existed between children from socioeconomically-advantaged backgrounds and children from socioeconomically disadvantaged backgrounds. Children from disadvantaged backgrounds have been shown to score much lower on measures of school-readiness, including the MRT, the measure of school readiness used in Mintons original study. The implication of a readiness gap is a future achievement gap that persists through elementary school, where advantaged children learn at an accelerated pace in comparison to disadvantaged children.

Judith Mintons sample included children from both advantaged and disadvantaged background, and new analyses of her original data years later tested whether viewing Sesame Street resulted in a change in the magnitude of the readiness gap between children from advantaged and disadvantaged backgrounds. There were concerns that viewing Sesame Street did nothing to reduce the readiness gap or perhaps even widened the readiness gap, thus having a higher impact on readiness of children from advantaged backgrounds than children from disadvantaged backgrounds.

The question of whether the impact of viewing Sesame Street is to increase the disparity between advantaged and disadvantaged children is question of whether there is an interaction between two EVs on the school readiness RVintervention/control group membership and advantaged/disadvantaged socioeconomic status. Hence, addressing this question required conducting a two-way ANOVA, and this test was conducted on Mintons data years later.

Here are the results:

Source | SS df MS F Prob>F

----------------+----------------------------------------------------

|

sesamestreet | 91.097201 1 91.097201 26.45 0.0000

ses | 1070.3531 1 1070.3531 310.76 0.0000

sesamestreet#ses | 88.374749 1 88.374749 25.66 0.0000

|

Residual | 861.06417 250 3.4442567

----------------+----------------------------------------------------

Total | 2039.7953 253 8.0624319

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| sesamestreet

ses | viewed not viewed Total

------------------+-----------------------------------

advantaged SES | 12.94118 10.27778 11.57143

|

disadvantaged SES | 7.020202 7 7.01087

|

|

Total | 8.533834 7.975206 8.267716

|

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(effect of SES for Sesame Street viewers)

---------------------------------------

| F df1 p

-------+-------------------------------

(1) | 16.83 1 0.0011 #

-------+-------------------------------

# Bonferroni adjusted p-values

(effect of SES for Sesame Street non-viewers)

---------------------------------------

| F df1 p

-------+-------------------------------

(1) | 5.92 1 0.0178 #

-------+-------------------------------

# Bonferroni adjusted p-values

1. a)Is there a significant main effect of viewing Sesame Street? Interpret the result of the test of this main effect. Refer to the relevant marginal means in the table of means above.

1. b)Is there a significant main effect of SES? Interpret the result of the test of this main effect. Refer to the relevant marginal means in the table of means above.

1. c)Is there a significant Sesame Street-by-SES interaction? Interpret the result of the test of the interaction effect, and the Bonferroni follow-up tests. Refer to the relevant cell means in the table of means above.

1. d)Is there evidence that viewing Sesame Street widened the readiness gap, narrowed the readiness gap, or had no impact on the readiness gap? Explain.