Question

There are many ways to measure the reading ability of children. Research designed to improve reading performance is dependent on good measures of the outcomes. One frequently-used test is the DRP, or Degree of Reading Power. It is known that the distribution of DRP scores is normally distributed. A researcher suspects that the mean score µ of all third-graders in Henrico County Schools is different from the national mean, which is 32. To test her suspicion, she administers the DRP to a random sample of 22 Henrico County third-grade students. Their scores are recorded in the following table:

40 26 39 17 42 18 24 43 46 27 19

47 19 26 37 34 15 45 41 39 31 46

(a) Find the t critical value for a 90% confidence interval for the true mean, µ, of the population.

(b) State and verify the conditions for the confidence interval.

(c) Compute and interpret the 90% confidence interval for the mean DRP score in Henrico County Schools. (You can find your point estimate and standard error in your calculator using the 1-Var Stats function. Compare your answers with a classmate to make sure you entered things in correctly!)

(d) Use the confidence interval you constructed in Part (c) to comment on whether you agree with the researcher’s suspicion. Explain your reasoning clearly.

Answer 1

$\bar x$ = 32.773

s = 10.858

a) At 90% confidence interval the critical value is t_0.05,21 = 1.721

b) The samples must be randomly selected from the population.

The sample values must be independent of each other.

The sample size should be no more than 10% of the population.

c) The 90% confidence interval is

$\bar x$ +/- t^* * s/

/TE

= 32.773 +/- 1.721 * 10.858/

22 V

= 32.773 +/- 3.984

= 28.789, 36.757

d) Since 32 lies in the confidence interval, so we don't agree with the researcher's suspicion.