in order to compare mean reaction times of basketball and football athletes, ind
ID: 3326521 • Letter: I
Question
in order to compare mean reaction times of basketball and football athletes, independent random samples of 16 observations are selected from each of the athlete populations. Reaction times distributed approximately normal and the two populations have equal variances. Their reaction times were tested with the following results: Basketball: X bar=1.2sec, S^2=1, football: X bar=1.3sec, S^2=1. What is the null and alternative hypothesis to test the claim that basketball players have faster reaction times than football players?
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1> 2
Alternative hypothesis: 1 < 2
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees offreedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.3536
DF = 30
t = [ (x1 - x2) - d ] / SE
t = - 0.283
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means (10) produced a t statistic of - 0.283. We use the t Distribution Calculator to find P(t < - 0.283)
Therefore, the P-value in this analysis is 0.39.
Interpret results. Since the P-value (0.39) is greater than the significance level (0.05), we cannot reject the null hypothesis.
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