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Construct the interval series, plot the graph of histogram and cumulative distribution function
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2. A study shows that length of the careers of professional basketball players are nearly normally distributed, with a mean of 6.1 years and a standard deviation of 1.8 years.
Scores of an achievement test show that it follows a normal distribution. Its mean is 78 with a standard deviation of 8. Find the interval between the middle 80% of the scores lie.
Between z = 0.46 and z = 2.57
Construct the 99% confidence interval for the population mean duration of the longdistance calls from the town.
In 2015, the average duration of long-distance telephone calls from a certain town was 9.4 minutes. A telephone company wants to perform a test to determine whether this average duration of long-distance calls has changed. Twenty calls, originating from the town, was randomly selected and the mean duration was 10.2 minutes with standard deviation 4.8 minutes. a) Using a 1% level of significance, Complete the following: i. Give the null and alternative hypothesis of this test. [2] ii. Determine the critical value(s) of this test. [2] iii. Compute the value of the test statistic. [2] iv. State the decision rule. [1] v. Give your decision based on the available sample evidence. [1] vi. Hence, state your conclusion
The manager of the Postal Services claims that 98 percent of their mail are delivered on time. He wants to test at the 1% significance level to determine whether the true proportion is less than 98 percent. i. Give the null and alternative hypothesis of this test. [2] ii. Determine the critical value(s) of this test. [2] iii. Compute the value of the test statistic. [2] iv. State the decision rule. [1] v. Give your decision based on the available sample evidence. [1] vi. Hence, state your conclusion
A recent survey showed that from a sample of 500 packages delivered by a Postal Service, 480 were delivered on time. a) Construct a 95% confidence interval for the proportion of all packages that are delivered on time by the Postal Service
A veterinary nutritionist developed a diet for overweight dogs. The total volume of food consumed remains the same, but one half of the dog food is replaced with a low-calorie “filler” such as canned green beans. Six overweight dogs were randomly selected from her practice and were put on this program. Their initial weights were recorded, and then they were weighed again after 4 weeks. At the 0.05 level of significance can it be concluded that the dogs lost weight?
Before 42 53 48 65 40 52
After 39 45 40 58 42 47
a. State the hypothesis and identify the claim of the researcher.
b. Find the critical value(s).
c. Compute for the mean of the differences, standard deviation of the differences
and test value.
d. Make a decision on the null hypothesis.
e. Make a decision on the claim of the researcher.
Suppose that a professional wrestler is selected at random among 90 wrestlers, where 35 are over 350 pounds, 20 are bad guys, and 15 are over 350 pounds and bad guys. What is the probability that the wrestler selected is over 350 pounds or a bad guy?
