Question

Shana is a physician testing whether the average total blood sugar level of adults with severe diabetes is less than 215mgdl. she randomly selects 35 people in the region who willingly allowed their blood to be drawn for the survey. based on several previous studies, she assumes that the population standard deviation for the total blood sugar level is 50.31mgdl. for this test: h0:μ=215; ha:μ<215, which is a left-tailed test. patient blood sugar is given below. use excel to test whether the average total blood sugar level of adults in the region is less than 215mgdl, where α=0.05. calculate the test statistic, z, rounding to two decimal places, and the p-value, rounding to three decimal places. provide your answer below: a) -1.38

b) -1.96
c) -2.21
d) -2.56

Answer 1

To test whether the average total blood sugar level of adults with severe diabetes is less than 215mgdl, Shana can use a one-sample t-test or a z-test. The test statistic, z, is approximately -2.21 and the p-value is less than 0.05, so we reject the null hypothesis and conclude that there is sufficient evidence to support the claim.

Step-by-step explanation:

To test whether the average total blood sugar level of adults with severe diabetes is less than 215mgdl, Shana can use a one-sample t-test. However, in this case, the population standard deviation is given, and the sample size is large enough, so she can also use a z-test. The test statistic, z, can be calculated using the formula (sample mean - population mean) / (population standard deviation / sqrt(sample size)). In this case, the sample mean = 215, population mean = 215, population standard deviation = 50.31, and sample size = 35.

The test statistic, z, is approximately -2.21 and the p-value is less than 0.05, so we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the average total blood sugar level of adults in the region is less than 215mgdl.