# One-Sample t-Tests. A Story Problem An educational consulting firm claims its new reading curriculum improves the mean reading score of children. Last.

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One-Sample t-Tests

A Story Problem An educational consulting firm claims its new reading curriculum improves the mean reading score of children. Last year the mean score in the school system (for all the students) was 100. For each of the following scenarios, do the data support the claim that the new curriculum improves the mean score?

Scenario 1 A random sample of 100 students was taught the new curriculum. Their mean score was 102 with an SD of 10.  Did this show significant improvement or just random fluctuation — sampling error?

Scenario 2 A random sample of 36 students was taught the new curriculum. Their mean score was 102 with an SD of 10.  Did this show significant improvement or just random fluctuation — sampling error?

Scenario 3 A random sample of 400 students was taught the new curriculum. Their mean score was 102 with an SD of 5.  Did this show significant improvement or just random fluctuation — sampling error?

Scenario 4 A random sample of 100 students was taught the new curriculum. Their mean score was 101 with an SD of 16.  Did this show significant improvement or just random fluctuation — sampling error?

Scenario 5 A random sample of 400 students was taught the new curriculum. Their mean score was 99 with an SD of 4.  What is your conclusion? (Hint: Should we use a one-tailed or two-tailed t-test?)

The Null Hypothesis  What was the null hypothesis for the story problem (in words, general idea)?  What was the formula that states the null hypothesis?  How do we use the null hypothesis to set up the formula for the test statistic (in this case, a t- test)?

Key Terms for Hypothesis Testing  Null hypothesis  Test statistic: How discrepant is the computed value (based on the sample) from the value expected if the null hypothesis is true?  Standard error  Critical value

More Key Terms  Comparing the test-statistic value to the critical value — is it discrepant enough?  Reject or fail to reject the null hypothesis.  P-value — probability of Type I error.  P-value must be small — the smaller the better (the higher the level of significance); less than.05 (that’s 5/100).

What a t-Test Can’t Tell Us  Whether the consultant is honest or not.  Whether the random sample (or other type of probability sample) was drawn correctly.  The cost (e.g., money or effort) of changing curricula — even if the new curriculum is significantly better, statistically, is it worth making the change?

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