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Question 1 Frequency distribution Question 2 435 to 510510 to 585585 to 660660 to 735735 to 810810 to 885 0 1 2 3 4 5 6 7 8 Histogram Number of pages found in book Frequency Question 3 Based on the above histogram, it is apparent that the shape is asymmetric owing to present of right skew. As a result, the distribution would be non-normal. 1
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Question 7 Question 8 Any data value less than¿¿−2σ__or greater than _¿+2σ__is to be considered as outliers. Outliers =None Question 9 Mean624.93 Standard deviation116.28 z value for Books less than 750 pages? Sample size30 Z score5.89 Z score = (x- mean) /(standard deviation / sqrt(sample size) Z score = (750-624.93)/(116.28/sqrt(30)) = 5.89 Question 10 Mean624.93 Standard deviation116.28 z value for Books has 350 pages? Sample size30 Z score-12.95 3
Z score = (x- mean) /(standard deviation / sqrt(sample size) Z score = (350-624.93)/(116.28/sqrt(30)) = 5.89 Question 11 The z score for 350 mean indicates that the standard deviation is -12.95 below the mean. Question 12 95% confidence interval Mean624.93 Standard deviation116.28 z value for 95% confidence interval1.96 Sample size30 Standard error = standard deviation / sqrt (sample size)116.28/sqrt(30)) =21.230 Margin of error = Z value * standard error= 1.96*21.230 = 41.61 Lower value of 95% confidence interval = Mean – Margin of error = 624.93 – 41.61 = 583.32 Upper value of 95% confidence interval = Mean + Margin of error = 624.93 – 41.61 = 666.54 95% confidence interval = [583.32666.54] Question 13 It can be said with 95% confidence that the mean pages of books in statistical book would lie between 583.32 and 666.54. Question 14 Alternative hypothesis H1:μ>560Mean number of pages is greater than 560. 4
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Null hypothesis H0:μ=560Mean number of pages is not greater than 560. Test statistics (Z score) = (x- mean) /(standard deviation / sqrt(sample size) Z score = (560-624.93)/(116.28/sqrt(30)) = -3.06 The p value = 0.001107 Given significance level = 0.05 Here p value less than significance level and hence,reject null hypothesis and accept alternative hypothesis.Therefore, it can be concluded that the mean number of pages in book is higher than 560. 5