Question

in a sample of 13 randomly selected high school seniors, the mean score on a standardized test was 1179 and the standard deviation was 168.2. further research suggests that the population mean score on this test for high school seniors is 1020. does the t - value for the original sample fall between - t_{0.95} and t_{0.95}? assume that the population of test scores for high school seniors is normally distributed.
the t - value of t = fall between - t_{0.95} and t_{0.95} because t_{0.95} = (round to two decimal places as needed.)

Explanation:

Step1: Calculate the t - value

The formula for the t - value is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\), where \(\bar{x} = 1179\) (sample mean), \(\mu=1020\) (population mean), \(s = 168.2\) (sample standard deviation), and \(n = 13\) (sample size).

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Step2: Find the critical value \(t_{0.95}\)

The degrees of freedom \(df=n - 1=13-1 = 12\). Using the t - distribution table, for a one - tailed test with \(\alpha=0.05\) and \(df = 12\), \(t_{0.95}=1.782\)

Answer:

The t - value of \(t = 3.41\) does not fall between \(-t_{0.95}\) and \(t_{0.95}\) because \(t_{0.95}=1.78\)