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Math Help - homework help: how do I solve hypothesis testing without standard deviation?

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    homework help: how do I solve hypothesis testing without standard deviation?

    Q7. Law enforcement officers in a city have claimed that over 40% of all robberies committed by those who have a history of drug abuse and/or alcohol abuse. The Journal of Research in Crime and Delinquency recently reported that in a random sample of 96 robberies, 40 were found to be committed by people who had drugs and/or alcohol abuse problems. Does this data substantiate the law enforcement officers’ claim at a 5% level of significance (i.e., alpha=0.05)? [8 points]

    since the 96 robberies is more than 30, I would use the z test. the z test requires a standard deviation. am i looking at this wrong?
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    Quote Originally Posted by jd254 View Post
    Q7. Law enforcement officers in a city have claimed that over 40% of all robberies committed by those who have a history of drug abuse and/or alcohol abuse. The Journal of Research in Crime and Delinquency recently reported that in a random sample of 96 robberies, 40 were found to be committed by people who had drugs and/or alcohol abuse problems. Does this data substantiate the law enforcement officers’ claim at a 5% level of significance (i.e., alpha=0.05)? [8 points]

    since the 96 robberies is more than 30, I would use the z test. the z test requires a standard deviation. am i looking at this wrong?
    Variance = \frac{\theta (1 - \theta)}{n} where \theta is the true proportion.

    But this leads to a probability statement that is difficult to invert, so a simple and quite good approximation is to take  \theta (1 - \theta) = \hat{\theta} (1 - \hat{\theta}) where \hat{\theta} is the sample proportion.
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    i have no idea what u said, but u did mention the proportion testing, so i pulled out the text and did it their way. can you check if I did it right?

    H0: p < or = 0.40
    H1: p > 0.40 (claim)
    alpha = 0.05
    critical value = 1.65
    p-hat = 40/96 = 0.416
    p = 0.40
    q = 0.60
    z = (p-hat - p)/sqr(pq/n) = (0.416 - 0.4)/sqr(0.40*0.60/96) = 0.33

    0.33 < 1.65

    there is not enough evidence to support the claim

    I'm sure I did it right, I'm just not too sure about the last part with the claiming and evidence part
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