EXAMPLE 6.15

Energy intake from sugar-sweetened beverages. Consumption of sugar-sweetened beverages (SSBs) has been positively associated with weight gain and obesity and negatively associated with the intake of important micronutrients. One study used data from the National Health and Nutrition Examination Survey (NHANES) to estimate SSB consumption among adolescents (aged 12 to 19 years). More than 2400 individuals provided data for this study.¹⁵ The mean consumption was 298 calories per day.

You survey 100 students at your large university and find the average consumption of SSBs per day to be 262 calories. Is there evidence that the average calories per day from SSBs at your university differs from this large U.S. survey average?

The null hypothesis is “no difference” from the published mean μ₀ = 298. The alternative is two-sided because you did not have a particular direction in mind before examining the data. So the hypotheses about the unknown mean μ of the students at your university are

H₀: μ = 298

H_a: μ ≠ 298

As usual in this chapter, we make the unrealistic assumption that the population standard deviation is known. In this case, we’ll use the standard deviation from the large national study, σ = 435 calories.

We compute the test statistic:

= −0.83

Figure 6.11 illustrates the P-value, which is the probability that a standard Normal variable Z takes a value at least 0.83 away from zero. From Table A, we find that this probability is

P = 2P(Z ≥ 0.83) = 2(1 − 0.7967) = 0.4066

That is, if the population mean were 298, more than 40% of the time an SRS of size 100 from the students at your university would have a mean consumption from SSBs at least as far from 298 as that of this sample. The observed is, therefore, not strong evidence that the student population mean at your university differs from that of the large population of adolescents.