<1> The heights of a random sample of 60 students showed a mean of 175 cm and a standard deviation of 7 cm. construct a 95% confidence interval for the mean height of all students.(173.23,176.77).
<2> Some one claimed that the mean height of all students is 178 cm. With the result from Problem <1>, do you accept or reject the claim?(reject).
<3> A cigarette manufacturer claims that his cigarettes have an average nicotine content of 1.83 milligrams. If a random sample of 8 cigarettes of this type shows a sample mean of 1.95 with sample deviation 0.22 milligrams, find 95% confidence interval for the population mean. Do you agree with the claim? (1.766,2.134)(yes).
<4> The mean and standard deviation for the GPA of a random sample of 100 students are 2.9 and 0.5 respectively. Find the 95% confidence interval for the average GPA of all students in the school.(2.802, 2.998).
<5> The contents of 7 similar containers of a commercial soap are 10.2, 9.8, 10.4, 9.8, 10.0, 10.2, and 9.6 liters. Find 95% confidence interval for the mean content of all such containers.(9.74,10.26).
<6> A sample of 10 cracker boxes gives a mean of 15.99 (ounces) and sample standard deviation 0.1. Use t distribution to find a 95% confidence interval for the population mean.(15.92,16.06).
<7> A survey of 90 families showed that 40 owned a gun. Find the 99% confidence interval of the true proportion of families who own a gun.(0.31,0.58)
<8> An insurance company is trying to estimate the average number of sick days that full-time food service workers use per year. A pilot study found the standard deviation to be 2.5 days. How large of a sample must be selected if the company wants to be 95% confident of getting an interval that contains the true mean with a max error of 1 day? (25).
<9> Let p be the real probability of getting head when tossing a given coin. We tossed 500 times and found 260 heads. Find the 95% confidence interval for p. How many times should we toss the coin in order to be 95% confident that our estimate of p is within 0.02? (0.476,0.564)(2401).
<10> A merchant claims that the average age of customers who purchase a certain brand of jeans is 15. A sample of 35 customers had an average age of 15.6 years with standard deviation of 1 year. At type I error 0.05, test the claim. (reject the null hypothesis).
<11>The average SAT score in Math is 500, with a standard deviation of 100. A special preparation course claims that it can increase scores. A sample of 100 students completed the course, and the average of their scores was 520. At type I error 0.05, test the claim. (reject the null hypothesis).
<12> In a random sample of 1000 homes in a city, it is found that 620 are heated by natural gas. Find a 95% confidence interval for the fraction of homes in this city that are heated by natural gas.(0.59,0.65).
<13> A travel agency claims that it books an average of at least 45 people per trip to Washington D.C. A sample of 15 trips showed a mean of 41 people booked and a standard deviation of 5. At type I error 0.05, test the claim. (reject the null hypothesis).
<14> The weights of 9 women who followed a new diet were recorded before and after a 4-week period ( kilogram ): Woman 1 2 3 4 5 6 7 8 9. Weight before 71 72 60 72 65 60 52 75 68. Weight after 68 73 56 69 60 57 48 67 62. Find the 95% confidence interval for the mean difference in the weight, assuming a normal distribution for the weights. If the company claims that the new diet will reduce a person's weight by 8 kilograms on the average in a 4-week period, do you agree? (1.99,5.79)(disagree).