Statistics Quiz

At most 43% of workers got their job through networking. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage). H0:pH0:p 

H1:pH1:p  Use the following codes to enter the following symbols:       ≥≥ enter >=       ≤≤ enter <=       ≠≠ enter !=

A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes. A local government office in a rural area randomly samples 100 elementary school children in their district and find an average one-way commute time of 38 minutes with a standard deviation of 8 minutes.

Which of the following is the correct set of hypotheses for testing if the average commute time of elementary school students in this district is different than the commonly cited standard of 30 minutes?

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H0: μ = 30; HA: x = 38

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HA: μ = 30; H0: x ≠ 30

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H0: μ = 30; HA: μ > 30

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H0: x = 38; HA: μ = 30

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H0: μ = 30; HA: μ ≠ 30

A New York Times article titled For Runners, Soft Ground Can Be Hard on the Body considered two perspectives on whether runners should stick to hard surfaces or soft surfaces following an injury. One position supported running on soft surfaces to relieve joints that were in recovery from injury. The second position supported running on hard surfaces since soft surfaces can be uneven, which may make worse those injuries a soft surface was intended to help.

Suppose we are given sufficient funds to run an experiment to study this topic. With no studies to support either position, which of the following hypotheses would be appropriate?

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Because there is uncertainty, we should postpone defining the hypotheses until after we collect data to guide the test.

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The second position makes the more sense, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the first position.

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The first position is more sensible, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the second position.

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Because we would be interested in any difference between running on hard and soft surfaces, we should use a two-sided hypothesis test.

If your null and alternative hypothesis are: H0:p=0.13H0:p=0.13  H1:p>0.13H1:p>0.13 Then the test is:

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two tailed

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right tailed

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left tailed

A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes.

A local government office in a rural area conducts a study to determine if elementary schoolers in their district have a longer average one-way commute time. If they determine that the average commute time of students in their district is significantly higher than the commonly cited standard they will invest in increasing the number of school busses to help shorten commute time. What would a Type 2 error mean in this context?

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The local government decides that the average commute time is 30 minutes.

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The local government decides that the data provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact 30 minutes.

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The local government decides that the data do not provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact higher than 30 minutes.

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The local government decides that the data do not provide convincing evidence of an average commute time different than 30 minutes, when the true average commute time is in fact 30 minutes.

Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses.

H0: the food is safe 

Ha: the food is not safe

The following is an example of what type of error?

The sample suggests that the food is safe, but it actually is not safe.

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type I

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type II

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not an error

If your claim is in the alternative hypothesis and you fail to reject the null hypothesis, then your conclusion would be:

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The sample data support the original claim

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There is sufficient evidence to warrant rejection of the original claim

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There is not sufficient evidence to warrant rejection of the original claim

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There is not sufficient sample evidence to support the original claim