In a test of the hypothesis that the population mean issmaller than 50, a random sample of 10 observations is selectedfrom the population and has a mean of 47.0 and a standard deviationof 4.1. Assume this population is normal.
a) Set up the two hypotheses for this test. Make sure you writethem properly.
b) Check the assumptions that need to hold to perform thishypothesis test.
c) Calculate the t-statistic associated with the sample.
d) Graphically interpret the p-value for this test, that is, i)draw a (nice) graph with a t-distribution (remember of the numberof degrees of freedom) ii) locate on the graph the t-statistic youfound in part (c) iii) mark the P-value on the graph
e) Calculate the P-value for this test.
f) Statistically interpret the P-value for this test.
g) Let the level of significance α = 2.5%. Using P-value, make aconclusion for your test (write a complete sentence for fullcredit).
h) Let the level of significance α = 2.5%. Find the relatedcritical value tα.
i) What is the rejection region (RR) implied by α = 2.5% ?
j) Draw the RR on your graph on page 1, part (d).
k) Using the RR, make a conclusion for your test (write acomplete sentence for full credit).
