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Company officials were concerned about the length of time a particular drug product retained its potency. A random sample of 10 bottles of the product was drawn from the production line and analyzed for potency (fresh). A second sample of 10 bottles was obtained and stored in a regulated environment for a period of 1 year (stored). They test  H0: the true mean potency for fresh bottles and for bottles stored for 1 year are the same H1: the true mean potency for fresh bottles and for bottles stored for 1 year are different Fill in the blanks by selecting from the dropdown menu. If the test determines that the true mean potency for fresh and the true mean potency for stored bottles are the same when they are actually different, then this is a [fill1] error. If the test determines that the true mean potency for fresh and the true mean potency for stored bottles are different when they are actually the same, then this is a [fill2] error. The [fill3] of the test is the probability that the test determines that the true mean potency for fresh and the true mean potency for stored bottles are different when they are different. The [fill4] of the test is the probability that the test incorrectly determines that the true mean potency for fresh and the true mean potency for stored bottles are different.

For hypothesis tests or confidence intervals for a mean, the theory behind the Central Limit Theorem is to allow the researcher to assume the sample comes from a normal population. Is this statement true or false?

Suppose the P value for the hypothesis test of    Vs.    is 0.018. For the same data, if we instead did a two-tailed test of    Vs.  , the p value would be 

Here is a copy of tables you might need for the exam. Click on the table (not the downarrow) to view the table within the spacer.  Z_T_CHITables.pdf

We are testing the null hypothesis

A World Campus administrator wants to test if more than 60% of all World Campus undergraduate students are first-generation college students. In a random sample of 75 World Campus undergraduate students, 51 are first-generation college students. What is the test statistic to test the administrator’s question? 

Please note that this question consists of three parts. Show all your work/explanation. Just giving the answer without adequate work/explanation may result in zero for the question.  The shoulder width of an adult male is normally distributed with a mean of 16.2 in and a standard deviation of 1.6 in. The standard coach seat on a plane is 17.2 inches wide. What percentage of adult males fit in such a seat without overflow? An engineer wants to design an airline chair to fit 98% of the male passengers. What should be the minimum width of the chair? Find the range, centered at the population mean, that contains 90% of the adult male’s shoulder breadths.

State if each of the below statement is either true or false.  

Please note that this question consists of six parts. Show all your work/explanation. Just giving the answer without adequate work/explanation may result in zero for the question.  A company makes insulation shields for electrical wires using four different types of machines. The company wants to evaluate the variation in the inside diameter dimensions of the shields produced by the machines. A quality engineer at the company randomly selects shields produced by each of the machines and records the inside diameter of each shield (in millimeters). She wants to determine whether or not the mean inside diameter is the same for the four machines. Use the provided partial output to answer the following questions. Write down the null and alternative hypotheses for testing whether or not the mean inside diameter is the same for the four machines. Clearly define any parameters you might use. Compute the Error Degrees of Freedom missing in the ANOVA output. Compute the Treatment Mean Square missing in the ANOVA output. Compute the F-value missing in the ANOVA output. At 5% significant level, is there sufficient evidence to claim that the mean inside diameter is different for at least one of the four machines. Explain your answer. The output for Tukey pairwise comparisons is given below. Based on the output Based on the grouping information output, is the mean inside diameter significantly different for machines B and C? Explain your answer. Based on Tukey simultaneous CIs, for which machines the mean inside diameter is significantly different from machine A? Explain your answer.

The scores on a test administered each year to many high school students are normally distributed with mean 515 and standard deviation 130. What percentage of scores are  above 645? [fill1] between 385 and 775? [fill2]