Calculations Shown

As discussed in the 8th Chapter of your text, one can use data from a random sample to test a claim or hypothesis about a population. For example one might want to test the claim that the mean age of all FHSU Elements of statistics students is at least 30 years.   In this activity, you will apply your understanding of hypothesis testing to actual data—the data collected in Activity 1a of this course.  This activity is designed to have you use the cleaned class data from Activity 4 to test some claims.  This data is given again to the right.
 NOTE:  In all three of these problems below, you are required to demonstrate your analysis process as described in the text, not just the final conclusion.  Also, as stated in the resources, there are requirements to applying hypothesis testing that should be checked–requirements that our collected data will actually fail to meet (for instance, the sample should be randomly selected from the population of interest).  However, for simplicity of the activity you MAY ASSUME that all requirements for hypothesis testing have been met in regard to the data collection process.
 Past enrollment data indicates that 20% of the students taking elementary statistics at FHSU have a family size of four people.  Is the enrollment in this semester’s virtual classes significantly more than this claim, as measured statistically?  Justify your answer through a formal hypothesis testing procedure on proportions with a 5% level of significance.  It is required that you give needed hypotheses and related statistical values below as well as statistical computations to the right (feel free to use the appropriate template from the Excel guide for Unit 3).  Then give a proper final interpretive conclusion below based on the statistical measures calculated and related to the context given.
It has been claimed that the mean age of all FHSUVirtualCollege statistics students is 28.65 years old.  Using the age data collected from this summer’s classes, test this hypothesis–that is does the collected data statistically support this claim or is the mean age likely different from 28.65 years old?  Justify your answer through a formal hypothesis testing procedure with a 0.10 level of significance.  Again, necessary claims, calculations, and values must be shown below and to the right.  Give your proper/final conclusion below.  (Hint:  Since the population s.d. is not known, make sure to realize the need to use the t-distribution for testing purposes.)
It has been claimed that the mean armspan of adults in the US is greater than 162.5 cm. Does the data of our statistics class support or contradict this claim?  Justify your answer through a formal hypothesis testing procedure with a P-value approach using a significance level of your choice.  Calculation of and interpretation of the P-value is required on this problem.  Give your final conclusion below.