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Using a single sample design with 28 participants they provide the program and then collect data on final grades. After the program, the sample mean was 90 and the sample standard deviation was 7. Conduct a t-test to determine if this is a significant difference from the population mean of 85 (the mean for ALL sections of Introductory Psychology from the previous semester). Set α= .05 and use a 2-tailed test.

1. In statistical notion, what is your null hypothesis?

2. Calculate your t-statistic.

Sagot :

From the information given, we have that:

1. The null hypothesis is: [tex]H_0: \mu = 85[/tex]

2. The t-statistic is t = 3.78.

Item 1:

We want to test if there is a significant difference from the population mean of 85, thus, at the null hypothesis, it is tested if the population mean is of 85, that is:

[tex]H_0: \mu = 85[/tex]

Item 2:

The t-statistic is given by:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

  • X is the sample mean.
  • [tex]\mu[/tex] is the value tested at the null hypothesis.
  • s is the sample standard deviation.
  • n is the sample size.

For this problem, we have that: [tex]X = 90, \mu = 85, s = 7, n = 28[/tex]. Then:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{90 - 85}{\frac{7}{\sqrt{28}}}[/tex]

[tex]t = 3.78[/tex]

The t-statistic is t = 3.78.

A similar problem is given at https://brainly.com/question/25193176

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