Question

Do various occupational groups differ in their diets? A British study of this question compared 86 drivers and 52 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.

	Drivers	Conductors
Total calories	2820 ± 45	2842 ± 46
Alcohol (grams)	0.23 ± 0.09	0.37 ± 0.15

What justifies the use of the pooled two-sample t test?

The similarity of the sample means suggests that the population standard deviations are likely to be similar.

The similarity of the sample standard deviations suggests that the population standard deviations are likely to be different.     

The similarity of the sample means suggests that the population standard deviations are likely to be different.The similarity of the sample standard deviations suggests that the population standard deviations are likely to be similar.

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.)

t =
df =
P-value =

Answer 1

Solution:-

The similarity of the sample standard deviations suggests that the population standard deviations are likely to be similar.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u_Conductors< u_Driver
Alternative hypothesis: u_Conductors > u_Driver

Note that these hypotheses constitute a one-tailed test.

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).

S.E = 7.9713
DF = 136

t = [ (x₁ - x₂) - d ] / SE

t = 2.76

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 produced a t statistic of 2.76

Therefore, the P-value in this analysis is 0.003

Interpret results. Since the P-value (0.003) is less than the significance level (0.05), hence we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that conductors consume more calories per day than do drivers.