3 probs.

Formulate a linear programming spreadsheet model and solve it using Solver. See attached file for full problem description.

Tangent Planes and Graphing Functions

Attached is a tutorial question in regards to tangent planes, I'm a little stuck on how to produce the equation of the tangent when it involves a Ln function. If someone can help me and graphically represent it, it would be greatly appreciated. I'm not sure whether Mathematica would be the best software to use. See attached file for full problem description.

Inference on Mean - Known Variance

In a manufacturing process, the diameter of the steel rods is the product characteristic. A random sample of 25 steel rods is taken and sample mean is 8.88 cm. The diameter is assumed to be normally distributed with standard deviation 1.25. (i) Find a 95% confidence interval for the true diameter. If the standard deviation is unknown and the sample standard deviation is 1.25, will the 95% confidence interval be narrower or wider? (ii) If we would like the difference between the true mean and the sample mean to be less than 0.15, what is the minimum number of steel rods that we need to sample. Use alpha = 0.05.

Proportion testing of crime rate using Minitab

Figures for the yearly crime rate (the number of crimes per 1,000 population) in Mississippi, USA from 1993 to 2002 are as follows: 1.35 1.63 2.33 2.41 2.63 2.93 3.41 3.26 3.64 4.51 (i) Display a normal probability plot using Minitab and test whether the data follow a normal distribution. Write down the null and alternative hypotheses. Draw your conclusion based on the p-value and use alpha = 0.05 (ii) Test, at the 1% level of significance, whether the yearly crime rate is over 2.5 crimes per 1,000 population.

Inference on Proportion

In a statistics lecture, students are asked whether or not they enjoyed doing statistics. Random sample of 50 students was taken and 30 of them said that they enjoyed doing statistics. The lecturer claimed that more than 50% of the students enjoyed doing statistics. (i) Test, at the 5% level of significance, whether or not the lecturer's claim is reasonable. State the null and alternative hypotheses of the test. (ii) Find a 95% and a 99% confidence intervals for the true proportion of students who enjoyed doing statistics. Which one is wider? Why? (iii) If the lecturer would like the difference between the true proportion and the sample proportion to be less than 5%, what i... click for more