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Home Question Bank Math Statistics Archive 2025 January 04

Statistics Questions from Jan 04,2025

Browse the Statistics Q&A Archive for Jan 04,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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What is a scatter plot? What is a scatter plot? A sample of 7 workers in one plant took the following times (in minutes) \( 15,10,11,11,6,12 \) and 12 to complete a certain task. A sample of 7 workers in a second plant took \( 16,14,12,10,10 \), 12 and 10 minutes respectively to complete the same task. (a) Construct a \( 95 \% \mathrm{Cl} \) for the mean time of workers in the first plant, and the mean time of workers in the second plant. (b) Construct a \( 95 \% \mathrm{Cl} \) for the difference in the two population means. Example 1 The mean and standard deviation for the fill weights of 100 boxes are 12.05 and 0.1 respectively. Find an \( 85 \% \) confidence interval (CI) for the mean fill weight of the boxes. OR \[ =(0.89 \leq \overline{\mathrm{P}} \leq 0.95) \] ONFIDENCE INTERVAL FOR THE DIFFERENCE OF TwO ROPORTIONS 1) In a survey to determine the spread of TB in a community. It was discovered that 280 were affected out of 540 . Construct the confidence Interval of the difference of two proportions, if the level of confidence \( i \) 90\%. SOLUTION \[ \begin{aligned} \mathrm{CI} & =\text { Estimator } \pm \text { Error } \\ & =\left(\overline{\mathrm{P}}_{1}-\overline{\mathrm{P}}_{2}\right) \pm \text { Error } \\ \mathrm{P}_{1} & =280 / 540=0.519 \end{aligned} \] Scanned by CamScan \[ \begin{aligned} \mathrm{P}_{2} & =260 / 540=0.481 \quad \mathrm{OR} \\ & =1-0519=0.481 \\ 1-\propto & =\frac{90}{100} \\ 1-\propto & =0.90 \\ & \propto=1-0.9=0.1 \\ \mathrm{n} & =540 \end{aligned} \] Level of confidence \( =90 \% \) Error \[ \begin{array}{l} =Z \frac{\alpha}{2} \times \operatorname{SE}\left(\bar{P}_{1}-\bar{P}_{2}\right) \\ =Z \frac{0.1}{2} \times \sqrt{\frac{P_{1}\left(1-P_{1}\right)}{n_{1}}+\frac{P_{2}\left(1-P_{2}\right)}{n_{1}}} \end{array} \] Fisher information for a Poisson \( (\theta) \) sample is \( \theta \) \( 0 e^{\theta} \) \( \ln (\theta) \) \( \theta^{2} \) \( \frac{\ln \theta}{n} \) If \( X_{1}, X_{2}, \ldots, X_{n} \sim \operatorname{Bin}(n, \theta) \), then one of the following estimators is baised for \( \theta \) \( \frac{X_{4}}{2}+\frac{X_{1}}{2} \) \( n \bar{X} \) O \( \frac{(n-1)!\sum X_{i}}{n!} \) None \( | \)\begin{tabular}{c|c} If \( X \sim U(0, \theta) \), then \( c(\theta)= \) \\ \( O \) & \( -\ln (\theta) \) \\ 0 & \( \ln (\theta) \) \\ 0 & \( -\ln \left(\frac{1}{\theta}\right) \) \\ 0 & None \\ 0 & \( \frac{1}{\theta} \) \\ \end{tabular} What is a scatter plot? (3) In a recent poll, 1,000 randomly selected adults were surveyed and \( 27 \% \) of them said that they use the Internet for shopping at least once a year. (a) Give two reasons why a sample is cullected rather than carrying out a census of the population. (b) Calculate the margin of error of the survey. Give your answer to three decimal places. (c) Construct a 95\% confidence interval for the proportion of adults who use the internet for shopping at least once a year.
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