To assess the accuracy of a laboratory scale, a standard weight known to weigh grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is grams if the scale has no bias). In previous studies, the standard deviation of the scale readings has been about gram. How many measurements must be averaged to get a margin of error of with confidence? Show your work.
The required number is .
Given in the question that, To assess the accuracy of a laboratory scale, a standard weight known to weigh grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is grams if the scale has no bias). In previous studies, the standard deviation of the scale readings has been about gram . We need to find that how many measurements must be averaged to get a margin of error of with confidence.
Population standard deviation
Margin of error
The formula to compute the sample size is:
The z-score at confidence level is calculated from the standard normal table like this,
The number of measurements is calculated as:
Running red lights A random digit dialing telephone survey of drivers asked, "Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?" Of the respondents, admitted that at least one light had been red.
(a) Construct and interpret a confidence interval for the population proportion.
(b) Nonresponse is a practical problem for this survey-only of calls that reached a live person were completed. Another practical problem is that people may not give truthful answers. What is the likely direction of the bias: do you think more or fewer than of the respondents really ran a red light? Why? Are these sources of bias included in the margin of error?
Teens and their TV sets According to a Gallup Poll report, % of teens aged to have TVs in their rooms. Here is part of the footnote to this report:
These results are based on telephone interviews with a randomly selected national sample of teenagers in the Gallup Poll Panel of households, aged to . For results based on this sample, one can say . . . that the maximum error attributable to sampling and other random effects is percentage points. In addition to sampling error, question-wording and practical difﬁculties in conducting surveys can introduce error or bias into the ﬁndings of public opinion polls.
(a) We omitted the conﬁdence level from the footnote. Use what you have learned to determine the conﬁdence level, assuming that Gallup took an SRS.
(b) Give an example of a “practical difﬁculty” that could lead to biased results for this survey.
1. In the company’s prior-year survey, 80% of customers surveyed said they were “satisfied” or “very satisfied.” Using this value as a guess for pˆ, find the sample size needed for a margin of error of 3% at a 95% confidence level.
What if the company president demands 99% confidence instead? Determine how this would affect your answer to Question 1.
You have measured the systolic blood pressure of an SRS of company employees. A confidence interval for the mean systolic blood pressure for the employees of this company is . Which of the following statements gives a valid interpretation of this interval?
(a) of the sample employees have systolic blood pressure between .
(b) of the population of employees have systolic blood pressure between .
(c) If the procedure were repeated many times, of the resulting confidence intervals would contain the population mean systolic blood pressure.
(d) The probability that the population mean blood pressure is between is 0.95.
(e) If the procedure were repeated many times, of the sample means would be between .
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