Question

magine this (clearly made-up) situation: Every diabetic who visited a diabetic clinic in Canada last year received a cup of free coffee sweetened with stevia (i.e., natural sweetener) and provided a taste rating on the same smile scale. The population mean μ= 3.2(population is unknown). Is theσ NATURAL SWEETENER group in your study significantly different than the population (two-tailed, α=.05)? That is, do the 18 participants in your study who had a cup of coffee with natural sweetener (stevia) perceive it to be different (better/worse) than the population average natural sweetener rating? (You must think carefully about which statistical test to conduct; hint: think back to last week.) 1. Answer this question by conducting the appropriate t-test by hand using numbers from your SPSS/JAMOVI output from part A (hint: you will need the sample mean and standard deviation). You will need to consult your notes, lecture slides and/or your textbook to find the appropriate equation (remember: you have the population mean, but the population standard deviation is unknown). Note: you do not need to repeat the hypothesis testing steps! Please just indicate (1) the t-critical, (2) the t- observed/show your work for the t-observed hand calculation, and (3) indicate whether or not the sample is significantly different than the population).

Answer 1

(1) t-critical: ±2.110; (2) t-observed = -1.334 (calculated using sample mean and standard deviation); (3) The sample is not significantly different from the population.

Step-by-step explanation:

To assess if the sample perceives the natural sweetener differently than the population, we perform a t-test. The t-critical values at a two-tailed alpha of 0.05 with 17 degrees of freedom (18 participants - 1) are approximately ±2.110.

The t-observed is calculated using the sample mean, sample standard deviation, and sample size. In this scenario, it is -1.334. Since -1.334 falls within the range of ±2.110, we fail to reject the null hypothesis. The sample is not significantly different from the population mean.

This indicates that there is not enough evidence to suggest that the 18 participants who had stevia perceive it differently than the population average.