Vaccines have to be stored within a certain temperature range in order to stay potent. You are on an engineering team that designs temperature sensors for monitoring the conditions that the vaccines will encounter en route and at their final destination. Your newly designed smart temperature sensor must pass two tests for it to be considered competitive: (1) the standard deviation in the use of the sensors is at most 0.02 degrees, and (2) the mean lifetime of your sensors exceeds that of the current best-selling product. (1) A sample of 10 observations from your temperature sensors gave a sample standard deviation of 0.012 degrees. Is there strong evidence to indicate that the standard deviation of temperature reading is less than 0.02 degrees? State and test the relevant hypotheses at a = 0.05 by using the rejection region method. State any necessary assumptions about the underlying distribution of the data. %3D

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Vaccines have to be stored within a certain temperature range in order to stay potent.
You are on an engineering team that designs temperature sensors for monitoring the
conditions that the vaccines will encounter en route and at their final destination. Your
newly designed smart temperature sensor must pass two tests for it to be considered
competitive: (1) the standard deviation in the use of the sensors is at most 0.02 degrees,
and (2) the mean lifetime of your sensors exceeds that of the current best-selling product.
(1) A sample of 10 observations from your temperature sensors gave a sample standard
deviation of 0.012 degrees. Is there strong evidence to indicate that the standard
deviation of temperature reading is less than 0.02 degrees? State and test the
relevant hypotheses at a = 0.05 by using the rejection region method. State any
necessary assumptions about the underlying distribution of the data.
(2) The following summary data are collected to compare the lifetime of your sensors
and the XYZ sensors (current best-selling product):
Sample Size Sample Mean Sample Variance
(day)
220
(day)
16
Your sensors
XYZ sensors
8
10
200
32
Is there strong evidence to indicate that the mean lifetime of your sensors exceeds
that of the XYZ sensors? Use a = 0.05. State and test the relevant hypotheses at
a = 0.05. Assume equal variances.
(3) Does the equal variance assumption in (2) seem reasonable? State and test the
relevant hypotheses at a = 0.05.
Transcribed Image Text:Vaccines have to be stored within a certain temperature range in order to stay potent. You are on an engineering team that designs temperature sensors for monitoring the conditions that the vaccines will encounter en route and at their final destination. Your newly designed smart temperature sensor must pass two tests for it to be considered competitive: (1) the standard deviation in the use of the sensors is at most 0.02 degrees, and (2) the mean lifetime of your sensors exceeds that of the current best-selling product. (1) A sample of 10 observations from your temperature sensors gave a sample standard deviation of 0.012 degrees. Is there strong evidence to indicate that the standard deviation of temperature reading is less than 0.02 degrees? State and test the relevant hypotheses at a = 0.05 by using the rejection region method. State any necessary assumptions about the underlying distribution of the data. (2) The following summary data are collected to compare the lifetime of your sensors and the XYZ sensors (current best-selling product): Sample Size Sample Mean Sample Variance (day) 220 (day) 16 Your sensors XYZ sensors 8 10 200 32 Is there strong evidence to indicate that the mean lifetime of your sensors exceeds that of the XYZ sensors? Use a = 0.05. State and test the relevant hypotheses at a = 0.05. Assume equal variances. (3) Does the equal variance assumption in (2) seem reasonable? State and test the relevant hypotheses at a = 0.05.
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