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You are testing whether students at your school are overweight. You sample 25 students and measure how much more they weigh than the average weight for their height. The mean of your sample is 5 lbs, and the standard deviation is 5 lbs.
Find a 99% confidence interval for the true population mean. (Round to THREE decimal places.)
A tobacco company advertises that the average nicotine content of its cigarettes is at
most 14 milligrams. A consumer protection agency wants to determine whether the
average nicotine content is in fact greater than 14. A random sample of 300 cigarettes
of the company’s brand yield an average nicotine content of 14.6 and a standard
deviation of 3.8 milligrams. Determine the level of significance of the statistical test of
the agency’s claim that 𝜇 is greater than 14. If 𝛼 = 0.01, is there significant evidence
that the agency’s claim has been supported by the data?
15 New York Times bestselling fiction books had a standard deviation of 6.17 weeks on
the list. 16 New York Times bestselling nonfiction books had a standard deviation of
13.1 weeks. At the 10% significance level, can we conclude there is a difference in the
variance? Is there a difference between the variances of the number of weeks on the
best seller lists for nonfiction and fiction books?
Find the probability that at most 5 defective bolts will be found in a box of 200 bolts if it is known that 2 per cent of such bolts are expected to be defective. (you may take the distribution to be Poisson)
Use generating functions to solve the recurrence relation an = 7an−1 −
16an−2 + 12an−3 + n4n
, where a0 = −2, a1 = 0, a2 = 5.
Use rules of inference to show that the hypotheses “If the weather is not
too hot or not too cold, then the game will be held and a prize-giving
ceremony will occur,” “If the game is held then the VC will give a speech,”
“The VC did not give a speech,” imply the conclusion “The weather was
too hot.”
What is nested Quantifier? Is order important for nested quantifier?
Explain your answer with appropriate example.
A shipment has a 100 tape recorders of which 10 of these units are defective. What is the
probability that among 5 tape recorders chosen for inspection one will be defective?
Given the function y=√x
a. Find the differential dy.
b. Evaluate dy and ∆y if x=1 and dx=∆x=1
c. Find the equation of the tangent line at x=1
d. Sketch the graph of the curve y=√x and the tangent line in the Cartesian Plane using a scale of 1 unit = 1cm. Show in your diagram the line segments dx, dy, and ∆y. (Note: the curve us an upper semi-parabola whose vertex is at the origin and concaving to the right. Use 0, 1, 4, and 9 as x-coordinates.)
An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a mean of 800 hours and a standard deviation 40 hours. Test the null hypothesis that =800 hours against the alternative ≠800 hours if a random sample of 20 bulbs have an average of 700 hours. Use alpha = 0.05 level of significance.
