18. In the past, all patrons of a cinema complex have spent an average of $5.00
ID: 3322703 • Letter: 1
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18. In the past, all patrons of a cinema complex have spent an average of $5.00 for popcorn and other snacks, with a standard deviation of $1.80. If a random sample of 32 patrons is taken, what is the probability that the mean expenditure of this sample is greater than $4.20? 19. For each of the following claims i) State the Null Hypothesis H, and the Alternate Hypothesis H ii) Indicate which is the claim. ili) Determine whether the reject region is left-tailed, right-tailed or two-tailed. a) A consumer magazine reports that the mean life of a dot-matrix printer is at least 3.5 years. b) A realtor claims that rent for studio apartments in new buildings in Brooklyn cannot be $1500 a month. c) A car dealer announces that the mean time for an oil change in its service department is less than 20 minutes. For questions 20 - 23 answer all the following questions: a)State the Null and Alternate Hypotheses b) Which is the claim? c) Describe the reject region as left tailed, right tailed or two-tailed. d) Will you use a z-test or a t-test? What is the critical value? e) Find the sample statistic. f) Do you reject or fail to reject the claim? Write out your decision in at least one sentence 20. A report by a restaurant reviewer claims that serving staff, at all casual dining restaurants in New Jersey, receive at least $100 in tips with a standard deviation of $15. Colleen, who works as a server, in a casual dining restaurant in New Jersey, believes this claim is wrong. She records her tips over a 30 day, period and finds that they average $93. Using a 1% significance level test the claim. 21. It is claimed that the average annual per person spending on all prescription drugs is $ 410 with a standard deviation of $45. A survey of 64 randomly selected individuals found that average annual per person spending was $425. Using a 5% significance level test this claim. 22. A used car dealer says that the mean price of all 2009 Toyota Camry in Atlanta is at least $16,200. To test this claim you search the Internet and get the prices of a random sample of 14, of these cars available in Atlanta. The mean price of these cars is $15,999 with a standard deviation of $1057. Is there enough evidence to reject the dealer's claim at the 5% significance level? Assume the population is normal. The help line at Wiley Publishers claims that the mean wait time to be connected is 6.8 minutes. You randomly select a sample of 19 callers and calculate their mean wait times to be 6.7 minutes with a standard deviation of 1.24 minutes. Is there enough evidence to reject the claim at a 5% significance level? Assume the population is normally distributed 23.Explanation / Answer
18.
mean = 5
std. dev. = 1.8
n = 32
P(X > 4.20)
= P(z > (4.2 - 5)/(1.8/sqrt(32)))
= P(z > -2.5142)
= 0.9940
19.
a)
H0: mu = 3.5
H1: mu > 3.5
Claim is the alternative hypothesis i.e. mu > 3.5
This is right tailed test, hence rejection region lies to the right.
b)
H0: mu = 1500
H1: mu not equals to 1500
Claim is the alternative hypothesis i.e. mu not equals to 1500
This is two tailed test, hence rejection region lies to the both sides of the curve
c)
H0: mu = 20
H1: mu < 20
Claim is the alternative hypothesis i.e. mu < 20
This is left tailed test, hence rejection region lies to the left.
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