The number of accidents per day were studied for 144 days in city A and for 100 days in city B. The mean number of accidents and the standard deviation were found to be 4.5 and 1.2 respectively for city A and 5.4 and 1.5 for city B. Is city B more prone to accidents than city A at 5% and 1% levels of significance?
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- Null Hypothesis (\(H_0\)): The mean number of accidents in city B is less than or equal to the mean number of accidents in city A (\(\mu_B \leq \mu_A\)). - Alternative Hypothesis (\(H_1\)): The mean number of accidents in city B is greater than the mean Show more…
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The Scottish Executive, Analytical Services Division Transport Statistics, compiles data on motorcycle accidents. During one year, the numbers of motorcycle accidents in Scotland were tabulated by day of the week for built-up roads and non-built-up roads and resulted in the following data. $$\begin{array}{l|c|c} \hline \text { Day } & \text { Built-up } & \text { Non built-up } \\ \hline \text { Monday } & 88 & 70 \\ \text { Tuesday } & 100 & 58 \\ \text { Wednesday } & 76 & 59 \\ \text { Thursday } & 98 & 53 \\ \text { Friday } & 103 & 56 \\ \text { Saturday } & 85 & 94 \\ \text { Sunday } & 69 & 102 \\ \hline \end{array}$$ a. Without doing any calculations, make an educated guess at which of the two data sets, built-up or non built-up, has the greater variation. b. Find the range and sample standard deviation of each of the two data sets. Compare your results here to the educated guess that you made in part (a).
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(b) The following figures give the prices in rupees of a certain commodity in a sample of 15 shops selected at random from a city A and those in a sample of 13 shops from another city B: City A 7.41 7.77 7.44 7.40 7.38 7.93 7.58 8.28 7.23 7.52 7.82 7.71 7.84 7.63 7.68 City B 7.08 7.49 7.42 7.04 6.92 7.22 7.68 7.24 7.74 7.81 7.28 7.43 7.47 Assume that the distribution of prices in the two cities is normal (i) Is it possible that the average price of city B is Rs. 7.20? (ii) Is the observed variance in the first sample consistent with the hypothesis that the standard deviation of prices in city A is Rs. 0.30? (iii) Is it reasonable to say that the variability of prices in the two cities is the same? (iv) Construct 95% confidence interval for the mean price of the commodity in city A and comment on the result obtained. (v) Construct 95 % confidence interval for the variability of price in city B and comment on the result obtained.
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