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Write the converse of the following statement. Then determine its validity.
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Answer:
1.) .399
2.) {.369, .429}
Step-by-step explanation:
The proportion of criminals in this sample that were caught was =.39944, .399 rounded to three decimal places.
To construct the confidence interval, you need three pieces of information: the statistic, the critical value, and the standard error.
The statistic is given in the first part of the problem with the proportion of criminals in the sample that were caught was .399.
The critical value, we are told, is the z equivalent of 90%, or 1.645. You can find this value using a z table or with the inverse normal function on a calculator.
Finally, we need the standard error. The formula for standard error for a proportion with a single population is so in this situation it would be
=.0183.
The confidence interval would be .399±.018×1.645 or .399±.030 {.369, .429}