Bowker and Lieberman (1972) gave the results for tests of two thermostats used in irons that were made by an old supplier and a new supplier. 19 thermostats were sampled from the old supplier and 23 thermostats were sampled from the new supplier. The actual temperatures measured with a thermocouple and were recorded. The sample from the old supplier had a mean of \( \bar{x}_{1}=549.3 \) and a standard deviation of \( s_{1}=10.4 \). The sample from the new supplier had a mean of \( \bar{x}_{2}=550.3 \) and a standard deviation of \( s_{2}=11.5 \). Determine the value of the pooled standard deviation \( s_{p} \) \( s_{p}=\square \) (Record to two decimal places.) Clear all Check answer
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It is weighted by the degrees of freedom of each group. The formula for the pooled standard deviation is: \[ s_p = \sqrt{\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}} \] where: - \(n_1\) and \(n_2\) are the sample sizes from the old and new suppliers, Show more…
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A manufacturer of electric irons produces these items in two plants. Both plants have the same suppliers of small parts. A saving can be made by purchasing thermostats for plant $B$ from a local supplier. A single lot was purchased from the local supplier, and a test was conducted to see whether or not these new thermostats were as accurate as the old. The thermostats were tested on tile irons on the $550^{\circ} \mathrm{F}$ setting, and the actual temperatures were read to the nearest $0.1^{\circ} \mathrm{F}$ with a thermocouple. The data are as follows: Find $95 \%$ confidence intervals for $\sigma_{1}^{2} / \sigma_{2}^{2}$ and for $\sigma_{1} / \sigma_{2}$ where $\sigma_{1}^{2}$ and $\sigma_{2}^{2}$ are the population variances of the thermostat readings for the new and old suppliers, respectively. Find $95 \%$ confidence intervals for $\sigma_{1}^{2} / \sigma_{2}^{2}$ and for $\sigma_{1} / \sigma_{2}$ where $\sigma_{1}^{2}$ and $\sigma_{2}^{2}$ are the population variances of the thermostat readings for the new and old suppliers, respectively.
One- and Two-Sample Estimation Problems
Maximum Likelihood Estimation
A manufacturer of electric irons produces these items in two plants. Both plants have the same suppliers of small parts. A saving can be made by purchasing thermostats for plant $B$ from a local supplier. A single lot was purchased from the local supplier and it was desired to test whether or not these new thermostats were as accurate as the old. The thermostats were to be tested on tile irons on the $550^{\circ} \mathrm{F}$ setting, and the actual temperatures were to be read to the nearest $0.1^{\circ} \mathrm{F}$ with a thermocouple. The data are as follows: Find a $95 \%$ confidence interval for $_{1} \sigma_{1}^{2} / \sigma_{2}^{2}$ and for $\sigma_{1} / \sigma_{2}$, where $\sigma_{1}^{2}$ and $\sigma_{2}^{2}$ are the population variances of the thermostat readings from the new and old suppliers, respectively.
A 1992 article in the Journal of the American Medical Association ("A Critical Appraisal of 98.6 Degrees F, the Upper Limit of the Normal Body temperature, and Other Legacies of Carl Reinhold August Wundrlich") reported body temperature, gender, and heart rate for a number of subjects. The temperatures for 25 female subjects follow: 97.7 97.2 97.4 97.6 97.8 97.9 98.0 98.0 98.3 98.1 98.2 98.3 98.3 98.4 98.4 98.4 98.5 98.6 98.6 98.7 98.8 98.8 98.9 98.9 99.0 Test the hypothesis H0 : μ = 98.6 versus H1 : μ ≠ 98.6, using α = 0.05. Round your answers to three decimal places (e.g. 98.765). (a) Calculate the sample mean and standard deviation. (b) Determine the test statistic t0. (c) Draw conclusion. H0.
Madhur L.
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