Reference no: EM132848425
1.On March 10, 2020, nine NBA games were played. The average number of points scored in those games was 226, with a sample variance of 122.5.
Assuming that the underlying distribution of the data is normal and that these observations are independent and identically distributed, construct a 90% confidence interval for the true mean number of points of an NBA game. lower bound=219.14 upper bound=232.86,lower bound=217.49 upper bound=234.51, lower bound=220.85 upper bound=231.15, lower bound=213.62 upper bound=238.38
2.From April 7-12, 2020, the Pew Research Center surveyed Americans about the likelihood of coronavirus significantly disrupting their ability to vote in the November presidential election. Of the 4,917 polled, 3,294 answered "Very Likely" or "Somewhat Likely."
Construct a 95% confidence interval for the population proportion of Americans who would answer this question with "Very Likely" or "Somewhat Likely." lower bound=0.657 upper bound=0.683, lower=0.665 upper=0.675, lower=0.652 upper=0.687, lower=0.643 upper=0.696
3.Professional tennis player John Isner is known for having a fast serve; his fastest recorded serve ever is 157.2 miles per hour. You randomly collect a sample of 10 of Isner's serves and observe the following speeds in miles per hour: 142, 143, 143, 144, 146, 146, 146, 147, 147, and 150. The standard deviation of his serve speed is known to be sigma = 3.
Assuming that the distribution of his serve speed follows a normal distribution, construct a 90% confidence interval for the true mean of his serve speed. lower=142.96 upper=147.84, lower=143.54 upper=147.26, lower=143.84 upper=146.96, lower=144.03 upper=146.77
4.A realtor named Robert Higner wants to estimate the true mean size of a master bath of new homes in Yolo county. In order to do this, Robert collects a random sample of 60 houses and finds that the sample average is 161.61 square feet and s = 12.83.
Construct a 95% confidence interval for the true mean square footage of master bathrooms in Yolo county. lower=157.15 upper=165.75, lower=158.30 upper=164.92, lower=158.85 upper=164.37, lower=159.46 upper=163.76
5.Vihaan wants to buy a private island. Before purchasing an island, Vihaan collects a small sample of data on cost per acre. The sample of 8 islands cost per acre is: $173503, $311219, $137943, $551198, $336016, $140520, $362863, $405515.
Assuming normality of the underlying distribution, construct a 90% confidence interval using this data for the true mean average price per acre of a private island. lower=122892.3 upper=481802.2, lower=181088.3 upper=423606.2, lower=205192.4 upper=399502.0, lower=229783.3 upper=374905.1.
6.At Indiana Dunes State park the maximum allowable standard for swimming in the lake are 235 colonies of E. coli per 100 ml of water (source). In order to measure this, each day 10 different measurements of E. coli are taken at different locations in the lake near the beach. On a given day, the 10 measurements were 118, 175, 190, 206, 207, 208, 249, 256, 260, and 289.
Assuming the underlying distribution of E. coli counts is normal, construct a 95% confidence interval for the true mean number of colonies of E. coli per 100 ml of water. lower=164.81 upper=266.79, lower=180.30 upper=251.30, lower=187.04 upper=244.56, lower=194.10 upper=237.50
7.In 2018, there were 79,704 defendants in federal criminal cases. Of these, only 1879 went to trial and 320 resulted in acquittals.
Construct an 80% confidence interval for the true proportion of federals cases that go to trial that result in acquittals. lower=0.148 upper=0.193, lower=0.153 upper=0.187, lower=0.159 upper=0.181, lower=0.164 upper=0.176
8.According to the United States Postal Service, First Class Mail International (letters) takes 6 to 20 days to deliver to their destination (source). In order to test this Greg in Chicago sent one letter to Madrid, Spain every Monday for 52 weeks and tracked how long each letter took to deliver. The average delivery time for these 52 letters was 11.81 days and with a sample standard deviation of 3.17.
Calculate a 75% confidence interval for the true mean delivery time of First Class Mail International letters from Chicago to Madrid. lower=10.68 upper=12.94, lower=11.09 upper=12.53, lower=11.30 upper=12.32, lower=11.51 upper=12.11
9.Asmae is interested in the average length of American movies. In order to estimate this quantity, she collects a random sample of 8 movies and with running times of (rounded to nearest minutes): 79, 90, 94, 95, 102, 102, 107, 117.
Use these data to construct an 85% confidence interval for the mean movie run length. (Assume normality of the underlying distribution). lower=84.04 upper=112.46, lower=88.65 upper=107.85, lower=90.56 upper=105.94, lower=91.69 upper=104.81
10.It's that time of year again at Isaac's Fireworks Store! New Year's! Sale! Sale! Sale! However, Isaac is less than excited because last year he had a lot of complaints about a large number of defective fireworks that he sold. Isaac wants to know what percentage of his firework stock is defective. First, he plans to test his bottle rockets, so he takes a sample of 200 randomly chosen bottle rockets and he tests them. Of the 200, 14 failed.
Construct a 95% confidence interval for the true proportion of bottle rockets that will fail. lower=0.024 upper=0.116, lower=0.035 upper=0.105, lower=0.040 upper=0.100, lower=0.047 upper=0.093