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Basic Statistics: Calculations for Hypothesis Testing & Probability

Hello,

I'm having difficulties setting up the problems, I'm understanding the formulas and concepts, but I would really appreciate your help!

For Questions 3 & 4, complete the following:
a) State the null and alternate hypotheses. Will we use a left-tailed, right-tailed, or two-tailed test? What is the level of significance?
b) Identify the sampling distribution to be used: standard normal or the Student's t. Compute the z or t value of the sample test statistic and sketch its location.
c) Find the P value for the sample test statistic.
d) Should we reject or fail to reject the null hypothesis?

Question 3
How productive are employees? One way to answer this question is to study annual company profits per employee. Let x1 represent annual profits per employee in computer stores in St. Louis. A random sample of n1 = 11 computer stores gave a sample mean of x1 = $25,200 profit per employee with sample standard deviation s1 = $8,400. Another random sample of n2 = 9 building supply stores in St. Louis gave a sample mean x2 = $19,900 per employee with sample standard deviation s2 = $7,600. Does this indicate that in St. Louis computer stores tend to have higher mean profits per employee? Use α = 0.01. (50 pts)

Question 4
A telemarketer is trying two different sales pitches to sell a carpet cleaning service. For Sales Pitch I, he contacted 175 people and 62 of these people bought the cleaning service. For Sales Pitch II, he contacted 154 people and 45 of these people bought the cleaning service. Does this indicate that there is any difference in the population proportions of the people who will buy the cleaning service, depending on which sales pitch he uses? Use α = 0.05. (50 pts)
Question 5
Weights of a certain model of fully loaded gravel trucks follow a normal distribution with a mean of 6.4 tons and a standard deviation of 0.3 tons. What is the probability that a fully loaded truck of this model is (45 points)
a. Less than 6 tons?
b. More than 7 tons?
c. Between 6 and 7 tons?

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The solution provides step by step calculations for the testing of hypotheses and normal probabilities. Formula for the calculation and interpretations of the results are also included.

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