False Null Hypothesis

1) If a judge acquits every defendant, the judge never commits a type I error. True False 

2) In hypothesis testing, we cannot prove that a hypothesis is true True False 

3) The power of a test is the probability that the test will reject a false null hypothesis True False 

4) Type II error is the probability of rejecting a true null hypothesis True False 

5) Which is not true of p Value a). If they are small, we want to reject H0 b). They must be specified before the sample is taken c). They show the change of type I error if we reject H0 

6) Given H0: μ ≥ 18 and H1 <18, we would commit type I error if we: a). Conclude that μ ≥ 18 when the truth is that μ <18 b). Conclude that μ <18 when the truth is that μ ≥ 18 c). Fail to reject μ ≥ 18 when the truth is that μ <18 

7) In a right failed test of hypothesis, for a population mean with 13 degrees of freedom, the value of the test statistic was 1.863 the p-Value is: a). Less than .025 b). Between .025 & .05 c). Between .05 & 0.1 d).Greater than 0.10 

8) A study over a 10 year period showed that a certain mammogram test had a 50% rate of false positives. This indicates that: a). About half the tests indicated cancer b). About half the test makes a cancerous turn c). About half the tests showed a cancer that did not exist d). About half the women tested actually had no cancer 

9) Which of the followings is incorrect? 1). H0 is rejected when the calculated p-Value is less than the critical value of the test 2). In a right-tailed test, H0 is rejected when the value of the test statistics exceed the critical value 3). The critical value of a hypothesis test is based on the researchers selected level of significance 

10) Which of the followings is not a value null hypothesis? 1). H0: μ ≥ 0 2). H0: μ ≤ 0 3). H0: μ ≠ 0 4). All the above 

11) In hypothesis testing type I error is a). Always equal to 5% b). Always smaller or equal to 5% c). The probability of rejecting H0 when H0 is true 

12) In hypothesis testing, type II error is 1). Equal to 1 – probability of committing type I error 2). Equal to 5% or more 3). The probability to accept H0 when H1 is true 

13) The probability of type I error α and the probability of type II error β are related as follows: 1). β 〉 α 2). β 〈 α 3). α + β = 1 4). None of the above 

14) For a given sample size, when the probability of type I error increases, the probability of type II error 1). Remains unchanged 2). Increases 3). Decreases 4). is impossible to determine without knowing the distribution 

15) Having a normal distribution with σ=3 we test the hypothesis H0: μ =20 and find that = 21, then the test statistic is 1). 0 2). 1.645 3). 1.96 4). can not be determined 

16) The level of significance 1). Is the probability of a false alarm 2). Can be any value between 0 & 1 3). Is the likelihood of rejection the null H0 4). Has all of the above characteristics 

17) The critical value: 1). Is calculated from the sample 2). Is usually .05 or .01 3). Divides the acceptance region from the rejection rejoin 4). Is determined by the test statistic 

18) What is the estimated standard error if x=44 n=500 π= .15