Question

The result of a hypothesis test is said to be "statistically significant" under all the following circumstances EXCEPT:

Group of answer choices

There is convincing evidence supporting the alternative hypothesis.

The P-value is less than alpha.

The difference observed between the sample result and the parameter value stated in the null hypothesis is important in the real world.

The difference observed between the sample result and the value stated in the null hypothesis is highly unlikely to be due to random chance.

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Question 21 pts

If the result of a statistical test is significant at the .05 then:

Group of answer choices

it is not significant at the .10 level.

it is also significant at the .01 level.

it is also significant at the .10 level.

it is not significant at the .01 level.

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Question 31 pts

The "power of a test" is the probability of concluding H_A when in fact H_A is true. The power of a test will decrease if:

Group of answer choices

Data is collected or measured in a more consistent fashion.

A larger sample is used.

There is low variability amongst the population being studied.

A lower significance level (alpha) is used.

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Question 41 pts

The significance level (alpha) represents all the following EXCEPT:

Group of answer choices

The threshold of evidence required before concluding the alternative hypothesis.

The chance of concluding the alternative hypothesis even when its false.

Your willingness to make a Type II error.

Your willingness to make a Type I error.

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Question 51 pts

In a medical test for a particular disease, a Type I error would be:

Group of answer choices

repeating the test over and over until the test comes back negative.

concluding a person has the disease when they really don't.

concluding a person doesn't have the disease when they really do.

biasing the result by using improper measuring techniques.

Answer 1

1. Suppose, we wish to test the equality of means of a measure of two populations (at a significance level, say, ). Let denote the means of the two populations 1 and 2 respectively. denote the Null hypothesis (Negation of the claim to be tested) and the Alternate hypothesis (Claim to be tested) respectively.

To test:

Vs

Conducting an appropriate statistical test to test the above hypothesis, suppose we get a result with p-value (the probability of obtaining an extreme result, as the one obtained, when the null hypothesis is true) less than the significance level  - p-value < . This implies that the if , were actually true, the probability of obtaining this result is very low. It has occured not just by random chance, there is an external factor acting on it. Hence, we reject at level,since, we have convincing evidence supporting .

Hence the correct option would be:

The difference observed between the sample result and the parameter value stated in the null hypothesis is important in the real world.

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Question 21:

If the result of a statistical test is significant at the .05:

i.e.say p-value = 0.032.

We find that the p-value is significant at 5% level. We also observe that this p- value 0.032 < 0.10 (But > 0.01). Thus, it is also significant at 10% level (But not at 1% level).   

Hence the correct option would be:

It is also significant at the .10 level.

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Question 31:

The "power of a test" is the probability of concluding Ha when in fact Ha is true. It is the ability to detect a significant result. We know that Power is nothing but 1 - (where, = Type II error) and also that as Type I error increases, type II error decreases. Hence, Power is directly inversely proportional to type I error. Thus, when a lower significance level (alpha) is used, the power increases. Similarly, the we obtain better results (test of increased power) when the variability in the data is low.Also, the larger the sample size, the larger the power.

Hence the correct option would be:

Data is collected or measured in a more consistent fashion.

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.Question 41:

The significance level (alpha) represents all the following EXCEPT:

Alpha may be defined as the Probability of rejecting a null hypothesis, when it is in fact,true. This is similar to the Type I error. But type II error is the probability of accepting a null hypothesis when it is false.

Hence the correct option would be:

Your willingness to make a Type II error.

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Question 51 pts

In a medical test for a particular disease, a Type I error would be:

Suppose we have to test whether the person has the disease.Here,  H0 would be the negation of the claim:

H0:Person does not have the disease Vs Ha:  Person has the disease We know that type 1 error is the probability of rejecting a null hypothesis, when it is in fact,true, hence, the correct option would be:

- Concluding a person has the disease when they really don't.