The mean BMI in patients free of diabetes has been reported as 28.2. An investig
ID: 3133130 • Letter: T
Question
The mean BMI in patients free of diabetes has been reported as 28.2. An investigator measured BMI in 12 patients who are free of diabetes and found a mean BMI of 31.7 with a standard deviation of 5.9. The investigator hypothesizes that the BMI in patients free of diabetes is higher than what has been reported. Is there evidence that the BMI is significantly higher that 28.2? Use a 5% level of significance. You must report the null and alternative hypotheses, calculate the test statistic (show your work), and give the conclusion including a comparison to alpha or the critical value to receive full credit.
Explanation / Answer
One sample t test for population mean
The mean BMI in patients free of diabetes has been reported as 28.2. An investigator measured BMI in 12 patients who are free of diabetes and found a mean BMI of 31.7 with a standard deviation of 5.9. The investigator hypothesizes that the BMI in patients free of diabetes is higher than what has been reported. Is there evidence that the BMI is significantly higher that 28.2? Use a 5% level of significance. You must report the null and alternative hypotheses, calculate the test statistic (show your work), and give the conclusion including a comparison to alpha or the critical value to receive full credit.
Solution:
Here, we have to use the one sample t test for checking the researchers claim whether the average BMI is significantly higher than 28.2 or not. The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: The average BMI in patients free of diabetes is 28.2.
Alternative hypothesis: Ha: The average BMI in patients free of diabetes is significantly higher than 28.2.
Symbolically the null and alternative hypothesis is given as below:
H0: µ = 28.2 versus Ha: µ > 28.2
This is a one tailed test. (Right tailed test)
The level of significance or the value of alpha is given as 5% or 0.05.
The test statistic formula is given as below:
Test statistic = t = (X-bar – population mean) / [SD/sqrt (n) ]
Test statistic = t = (31.7 – 28.2) / [ 5.9 / sqrt (12) ] = 2.054976
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
28.2
Level of Significance
0.05
Sample Size
12
Sample Mean
31.7
Sample Standard Deviation
5.9
Intermediate Calculations
Standard Error of the Mean
1.7032
Degrees of Freedom
11
t Test Statistic
2.0550
Upper-Tail Test
Upper Critical Value
1.7959
p-Value
0.0322
Reject the null hypothesis
Here, we get the p-value as 0.0322 which is less than the given level of significance or alpha value 0.05, so we reject the null hypothesis that the average BMI in patients free of diabetes is 28.2, this means we conclude that the average BMI in patients free of diabetes is significantly higher than 28.2.
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
28.2
Level of Significance
0.05
Sample Size
12
Sample Mean
31.7
Sample Standard Deviation
5.9
Intermediate Calculations
Standard Error of the Mean
1.7032
Degrees of Freedom
11
t Test Statistic
2.0550
Upper-Tail Test
Upper Critical Value
1.7959
p-Value
0.0322
Reject the null hypothesis
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.