Question

As a part of her studies, floretta gathered data on the lifespan of 24 fruit flies. she works through the testing procedure: h0:μ=32; ha:μ<32 α=0.02 the test statistic is t0=x¯−μ0sn√=−1.956. the critical value is −t0.02=−2.177. at the 2% significance level, does the data provide sufficient evidence to conclude that the mean lifespan of fruit flies is less than 32 days?

Answer 1

Floretta's test statistic of -1.956 does not exceed the critical value of -2.177 at the 2% significance level, thus we fail to reject the null hypothesis and conclude that the data does not show that the mean lifespan of fruit flies is less than 32 days.

Step-by-step explanation:

To determine whether the data provides sufficient evidence at the 2% significance level to conclude that the mean lifespan of fruit flies is less than 32 days, we look at the calculated test statistic and compare it with the critical value. Floretta's data resulted in a test statistic (t0) of -1.956. The critical value for a one-tailed test at the 2% significance level (α = 0.02) is -2.177.

Since the test statistic is not more extreme than the critical value (-1.956 > -2.177), we fail to reject the null hypothesis (H0: μ = 32). Therefore, the data does not provide sufficient evidence at the 2% significance level to conclude that the mean lifespan of fruit flies is less than 32 days.