Commute times in the U. S. are heavily skewed to the right. We select a random sample of 200 people from the 2000 U. S. Census who reported a non-zero commute time. In this sample the mean commute time is 27.5 minutes with a standard deviation of 18.9 minutes. Can we conclude from this data that the mean commute time in the U. S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance. What is the p -value for this hypothesis test?

Step-by-step explanation:

Given that:

The population mean = 30

The sample size n = 200

The sample-mean = 27.5

The sample standard deviation s = 18.9

The level of significance ∝ = 0.05

The null hypothesis and the alternative hypothesis can be written as:

Since the alternative hypothesis indicates < sign, then this test is left-tailed

The  t-test statistics is:

t = -1.871

The p-value = P(t< -1.871)

From the standard normal t tables

The p-value = 0.0314

Thus, since the p-value is less than the level of significance ∝ = 0.05, then we reject the null hypothesis.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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p

step-by-step explanation: