So one way to think about this, we wanna find the critical value, we wanna find the z, that leaves not 6% unshaded in, but leaves 3% unshaded in. For a given z, they'll say, what is the total area going all the way from negative infinity up to including z standard deviations above, above the mean? So when you look up a lot of z-tables, they will give you, they Because a lot of z-tables will actually do something like this. If you're using a calculator function what yourĬalculator function does. And you should alwaysīe careful which type of z-table you're using or Now all we have to really do is look it up on a z-table, but even there we have to be careful. So this distance right over here, where this is 94%, this number of standard deviations, that is z star right over here. But how many standardĭeviations above and below the mean in order to capture 94% of the probability? 94% of the area. It which would actually be our true population parameter, which we do not know. Needed to think about is, assuming that the samplingĭistribution is roughly normal, and this is the mean of But the key question here is, what is our z star? And what we really Times the standard error of the statistic.
But we don't know that, so we multiply that Of the sample proportions, well then you actually have to know the population parameter.
#Finding p hat of two stats stat crunch plus#
So plus or minus some critical value times and what we doīecause in order to actually calculate the true standard deviation of the sampling distribution We're gonna think about which z star because that'sĮssentially the question, the critical value. So it's that one sample proportion that she was able to calculate, plus or minus z star, and Now in this particular situation, our statistic is p hatįrom this one sample that Elena made. That times the standard deviation of the statistic, of the statistic. Many standard deviations for the samplingĭistribution do we wanna go above or beyond? So the number of standardĭeviations we wanna go, that is our critical value, and then we multiply Minus around that statistic, plus or minus around that statistic, and then we say okay how So we take our statistic, statistic, and then we go plus or It could be if we're trying toĮstimate the population mean. Let me just write this in general form, even if we're not talkingĪbout a proportion. I keep doing this over and over again, that 90, that roughlyĩ4% of these intervals are going to overlap with our Interval around that one, that 94% that roughly as That's the confidence interval around that one, maybe if we were to do it again, that's the confidence And remember a confidence interval, at a 94% confidence level means that if we were to keep doing this, and if we were to keepĬreating intervals around these statistics, so maybe But then we also wannaĬonstruct a confidence interval. This case it's a sample, a random sample of 200 computers, we take a random sample, and then we estimate this by calculating the sample proportion. We don't know what that is,īut we try to estimate it. Proportion of computers that have a defect. Remember, the whole pointīehind confidence intervals are we have some true population parameter, in this case it is the Little reminder of what a critical value is. You to pause this video, let me just give you a
Star should Elena use to construct this confidence interval? So before I even ask A random sample of 200Ĭomputers shows that 12 computers have the defect. More information is available in the help file through StatCrunch.That Elena wants to build a one-sample z interval toĮstimate what proportion of computers produced at aįactory have a certain defect. Select the columns for the expected counts.Select the columns for the observed counts.Choose Stat > Goodness-of-fit > Chi-Square test.Enter the observed counts in the first column, and the expected counts in the second column.You'll need to calculate the expected counts based on the assumed distribution.Chi-Square Goodness-of-Fit Test Using StatCrunch Step 6 : No, there is clearly not enough evidence based on this sample to say that the distribution is different from what the company claims. Step 5 : Since the P-value is much larger than α, we do not reject the null hypothesis. of colors does not follow the company's claim Notice that all expected counts are at least 1, and none are less than 5.
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