STATISTICS AND PROBABILITY?

For each of the following problems, please provide the requested information.

(a) State the null and alternate hypotheses and the level of significance. Is the test

left-tailed, right-tailed, or two-tailed?

(b) Identify the appropriate sampling distribution: the standard normal or the

Student鈥檚 t. What is the value of the sample test statistic?

(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the

area corresponding to the P-value.

(d) Find the critical value(s).

(e) Based on your answers for parts (a) through (d), will you reject or fail to reject

the null hypothesis? Interpret your conclusion in the context of the application.

1. A large furniture store has begun a new ad campaign on local television. Before the

campaign, the long term mean daily sales were $24,819. A random sample of 40

days during the new ad campaign gave a sample mean daily sale of = $25,910.

Does this indicate that the population mean daily sales is now more than $24,819?

Use a 1% level of significance. Assume 蟽 = $1917.

2. A new bus route has been established between downtown Denver and Englewood,

a suburb of Denver. Dan has taken the bus to work for many years. For the old bus

route, he knows from long experience that the mean waiting time between buses at

his stop was ! = 18.3 minutes. However, a random sample of 5 waiting times

between buses using the new route had mean = 15.1 minutes with sample

standard deviation s = 6.2 minutes. Does this indicate that the population mean

waiting time for the new route is less than what it used to be? Use 伪 = 0.05. Assume

x is normally distributed.

3. How tall are college hockey players? The average height has been 71 inches. A

random sample of

14 hockey players had a mean height of 72.5 inches. We may assume that x has a

normal distribution with 蟽 = 0.9 inches. Does this indicate that the population mean

height is different from 71 inches? Use 5% level of significance.

4. How long does it take to have food delivered? A Chinese restaurant advertises that

delivery will be no more than 30 minutes. A random sample of delivery times is

shown below. Based on this sample, is the delivery time greater than 30 minutes?

Use a 5% level of significance. Assume that the distribution of delivery times is

normal.

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39 32 28 42 25 26 30STATISTICS AND PROBABILITY?
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