You believe that the mean BMI for college students is less than 25. The population standard deviation of BMI is unknown. You select a sample of size 30 and compute the sample mean to be 23.9 with a sample standard deviation of 3. What are the appropriate hypotheses? A. Null Hypothesis: μ< 25 Alt Hypothesis: μ= 25 B. Null Hypothesis: μ=23.9 Alt Hypothesis: μ < 23.9 C. Null Hypothesis: μ=25 Alt Hypothesis: μ>25 D. Null Hypothesis:μ=25 Alt Hypothesis:μ < 25

Answer:D. Null Hypothesis:μ=25 Alt Hypothesis:μ < 25Step-by-step explanation:Previous concepts and notationA hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".[tex]\bar X= 23.9[/tex] represent the sample mean[tex]s=3[/tex] represent the sample standard deviationn=25 represent the sample selectedSolution The claim that we want to test is that: "You believe that the mean BMI for college students is less than 25". So this statement needs to be on the Alternative hypothesis ([tex]\mu <25[/tex]) and the Null hypothesis would be the complement ([tex]\mu =25[/tex]) or ([tex]\mu \geq 25[/tex]).So the best option on this case is:D. Null Hypothesis:μ=25 Alt Hypothesis:μ < 25