Question

Psy. 230 T-tests  

present the 5-step hypothesis process, enter data into SPSS to obtain the SPPS outputs, and identify the results using the correct APA statement format, including implications. Don't forget to include:

• stating your null hypothesis, alternate hypothesis, defining the critical regions, and drawing out your critical regions in a t-distribution.
• your SPSS outputs.
• reporting the descriptive statistics for each group, the t-statistic, df, p-value, and confidence intervals.
• showing your effect size calculations, including an interpretation of what the effect size 'means'.
• reporting whether the differences between the conditions/ groups was/was not significant. Present your findings in a narrative and include tables, if appropriate.    
• a few sentences about what the results from this study means and its implications.

Individuals may work together, but each individual must submit their own findings and implications (your wording should be different than your group members.) If you work in a group or with others, include the names of your group members on your paper.  

Problem #1

Research examining the effects of preschool childcare has found that children who spent time in day care, especially high-quality day care, perform better on math and language tests than children who stay home with their mothers. In a typical study, a research obtains a sample of n=10 children who attended day care before starting school. The children are given a standardized math test for which the population mean is 50. The scores for the sample are as follows: 53, 57, 61, 49, 52, 56, 58, 62, 51, 56. Is this sample sufficient to conclude that the children with a history of preschool day care are significantly different from the general population? Use a two-tailed test with an alpha=.01.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u = 50
Alternative hypothesis: u 50

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 1.34371

DF = n - 1

D.F = 9
t = (x - u) / SE

t = 4.09

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 9 degrees of freedom is less than -4.09 or greater than 4.09.

Thus, the P-value = 0.003

Interpret results. Since the P-value (0.003) is less than the significance level (0.01), we have to to reject the null hypothesis.

from the above test we have sufficient evidence in the favor of the claim that the children with a history of preschool day care are significantly different from the general population.