Each of the following is a confidence interval for ? = true average (i.e., population mean) resonance frequency (Hz) for all tennis rackets of a certain type: (110.4, 111.6) (110.1, 111.9) (a) What is the value of the sample mean resonance frequency? Hz (b) Both intervals were calculated from the same sample data. The confidence level for one of these intervals is 90% and for the other is 99%. Which of the intervals has the 90% confidence level, and why? The first interval has the 90% confidence level because it is a wider interval. The second interval has the 90% confidence level because it is a wider interval. The second interval has the 90% confidence level because it is a narrower interval. The first interval has the 90% confidence level because it is a narrower interval.
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Let's use the first interval (110.4, 111.6): Sample mean = $\frac{110.4 + 111.6}{2} = \frac{222}{2} = 111$ Hz So, the sample mean resonance frequency is $\boxed{111}$ Hz. (b) A higher confidence level corresponds to a wider interval because it covers a larger Show more…
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The two intervals (113.5, 114.5) and (113.3, 114.7) are confidence intervals for ÎĽ = mean resonance frequency (in hertz) for all tennis rackets of a certain type. The two intervals were calculated using the same sample data. (a) What is the value of the sample mean (in hertz) resonance frequency? (b) The confidence level for one of these intervals is 90%, and for the other it is 99%. Which is which, and how can you tell? The 99% confidence interval is than the 90% confidence interval, because the t critical value for 99% confidence is than the t critical value for 90% confidence. Therefore, the 90% interval is Hz and the 99% interval is Hz.
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The two intervals (114.4,115.6) and (114.1,115.9) are confidence intervals for $\mu=$ mean resonance frequency (in hertz) for all tennis rackets of a certain type. The two intervals were calculated using the same sample data. a. What is the value of the sample mean resonance frequency? b. The confidence level for one of these intervals is $90 \%,$ and for the other it is $99 \%$. Which is which, and how can you tell?
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