A matched pairs design was used to compare test scores in a statistics course. Twenty-four students were chosen randomly from a large class. For each chosen student, their test 1 and test 2 scores were recorded. A 95% confidence interval for the difference in test scores was constructed, along with the corresponding 2-sided p-value was given as [−0.70,10.45], and the 2-sided p-value =0.084.How does one determine whether or not this result is statistically significant at the 5% level of significance?Also, if a 90 confidence interval was constructed instead of a 95% one, would it contain 0?Would appreciate some clues.

Question

svirajueh · Accepted Answer

1) For testing       H    0    :  δ  =  0 vs.       H    a    :  δ  ≠  0  ,, where the population difference in test 1 and test 2 scores is μ1−μ2=δ, one does not reject H0 at level 5% if the two-sided P-value exceeds 5%. Because your P-value is 0.084&amp;gt;0.05 you do not reject.2) Another criterion for failing to reject in (1) is that the 95% confidence interval (CI) contains 0. The CI can be considered an interval of &#039;acceptable&#039; values of δ.3) The 95% CI in (2) is of the form             D      ¯        ±      t    ∗        s    D        /        n    ;; where             D      ¯       is the sample mean of the observed differences       D    i    =      X    i    −      Y    i    ,, where       X    i   and       Y    i   the ith students difference in test 1 and test 2 scores; sD is the the sample standard deviation of the       D    i  ; n=24; and t∗=2.069 cuts 2.5% of the probability from the upper tail of Student&#039;s t distribution with n−1=23 degrees of freedom.For the same data, a 90% CI would be the same, except that you would use t∗=1.714, which cuts 5% of the probability from the upper tail of the same distribution. I will leave it to you to determine what difference the change from t∗=2.069 to t∗=1.714 would make in the width of the CI.

A matched pairs design was used to compare test scores in a statistics course. Twenty-four students

Answered question

Answer & Explanation

New Questions in College Statistics