Do various occupational groups differ in their diets? A British study of this qu
ID: 3356423 • Letter: D
Question
Do various occupational groups differ in their diets? A British study of this question compared 89 drivers and 57 conductors of London double-decker buses. The conductors' jobs require more physical activity. The article reporting the study gives the data as "Mean daily consumption ± (se)." Some of the study results appear below.
Is there significant evidence at the 5% level that conductors consume more calories per day than do drivers? Use the pooled two-sample t test to obtain the P-value. (Give answers to 3 decimal places.)
Drivers Conductors Total calories 2820 ± 44 2845 ± 49 Alcohol (grams) 0.24 ± 0.11 0.35 ± 0.02Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Conductors< Driver
Alternative hypothesis: Conductors > Driver
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 of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 7.992
DF = 144
t = [ (x1 - x2) - d ] / SE
t = 3.13
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size 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 produced a t statistic of 3.13.
Therefore, the P-value in this analysis is 0.0011
Interpret results. Since the P-value (0.0011) is less than the significance level (0.05), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that there is significant evidence at the 5% level that conductors consume more calories per day than do drivers.
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