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# Hypothesis Tests and Test Statistic

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1. (1 point) The Dick Tracy Co. has developed micro-miniaturized circuitry that will enable them to produce a wristwatch-sized video-telecommunicator. Research and development costs are believed to be high, and the company is uncertain whether it should proceed. The company has a strategic alliance with Cells-R-Us, a national provider of cellular telephone services, so a moderate-to-large sample of current cell phone customers is possible. The Marketing Department of the Dick Tracy Co. has developed a survey, which contains a list of possible features of next-generation telecommunicators, including compactness, ease of use, internet access, audio downloading/playing, video image downloading/video imaging, voice messaging, text messaging, et al. Survey respondents will be asked to rank order these features, first on the basis of personal preference, and then on the basis of willingness to pay a premium for them. From the perspective of the Dick Tracy Co., what are a null and an alternative hypothesis based on the perceived results of the survey?

2. (4 points) A TV manufacturer purchases picture tubes from independent suppliers, and contractually requires that the tubes have an average life of at least 550 hours. The firm received a shipment of tubes from a supplier, tested 25 tubes, and found that the average tube life was 535 hours with a sample standard deviation s = 37 hours.

1. What is the appropriate hypothesis test to determine if the shipment should be accepted or rejected? State the hypotheses.
2. What is the test statistic? Compute its value.
3. What is the critical value if the hypothesis test is conducted at the 5% level of significance? How does the computed value of the test statistic (from b.) compare with the critical value? Show on a sketch.
4. Should the shipment be accepted or rejected? Why?

https://brainmass.com/statistics/hypothesis-testing/research-249919

#### Solution Summary

The solution examines hypothesis testing and determines test statistics. The critical value of a hypothesis is determine with a 5% level of significance.

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## Statistical Hypothesis Testing: Crusty The Clown' Cereal

1. The sales of Crusty The Clown cereal since 2000 are:

Year Code Sales
(\$ millions)
2000 1 5
2001 2 7
2002 3 6
2003 4 10
2004 5 12

What is the sales forecast for 2005?

2. The owner of a car dealership wants to determine whether there is a relation between the income level and the type of vehicle purchased in their dealership. He randomly sampled 500 car buyers and obtained the following data:

Income Level SUV/Minivan Midsize Compact
up to \$30K/yr 13 71 106
\$30K-\$60K 33 76 45
more than \$60K/yr 66 59 31

At the .05 level of significance, determine whether there is a relation between the income level and the type of vehicle purchased. Show your work step by step.

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