null and alternative hypotheses

This Assignment has two parts. Part 1 has questions about probability calculations. Part 2 has questions about hypothesis testing. You will use Excel only in Question 6. All other questions should be calculated manually. Follow all instructions carefully.

Type in your calculations. Pictures of hand written work are not acceptable.

Part 1 Question 1

In a class where the exam averages are normally distributed, the mean score is 75 and the standard deviation is 10. If you want to find out the probability that a randomly picked student has scored 105 or above, what is the z-value that you should look up on the normal distribution table?

Question 2

According to a report by Scarborough Research, the average monthly household cellular phone bill is $73. Suppose local monthly household cell phone bills are normally distributed with a standard deviation of $11.

a. What is the probability that a randomly selected monthly cell phone bill is less than $95?

b. What is the probability that a randomly selected monthly cell phone bill is between $62 and $84?

Question 3

A Travel Weekly International Air Transport Association survey asked business travelers about the purpose for their most recent business trip. 19% responded that it was for an internal company visit. Suppose 950 business travelers are randomly selected.

a. What is the probability that more than 20% of the business travelers say that the reason for their most recent business trip was an internal company visit?

b. What is the probability that between 18% and 20% of the business travelers say that the reason for their most recent business trip was an internal company visit?

GB513: Business Analytics

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GB513: Business Analytics

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Part 2 Question 4

Suppose a study reports that the average price for a gallon of self-serve regular unleaded gasoline is$3.16. You believe that the figure is higher in your area of the country. You decide to test this claimfor your area of the United States by randomly calling gasoline stations. Your random survey of 25 stations produces the following prices (all in dollars). Assume gasoline prices for a region are normally distributed.

Did the data you obtained provide enough evidence to reject the claim? Use a 1% level ofsignificance.

Make sure you clearly state both the null and the alternative hypotheses in full sentences. Following your calculations, clearly state the conclusion in the same manner (do not simply say “accept/reject null”) and explain how you arrived at this conclusion (based on which metrics).

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