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Suppose you randomly choose a sample of 25 observations from a normal distribution. You then use those observations to estimate the mean of the population.
a. Assuming that we would consider anything from 159 to 161 as "equal to 160," and that we know that the standard deviation of the population is 1.0, estimate the probability that we will be able to determine that the mean is different than 160 if it actually is different than 160. Use α = 0.05. (Hint: this is equivalent to saying, "what is the probability that we will reject the null hypothesis given that it is false?")b. If the mean of the observations is 158.7, what would you guess the mean of the population is (on the basis of the sample)? (I do not want the confidence interval - just report your estimate of the population mean.)c. Suppose the population is N(160.0, 1.2). It is possible that you could extract a sample from that population such that a hypothesis test on that sample would reject the null hypothesis, even though it is true. If we use α = 0.01, what are the chances of this happening? (Hint: this is equivalent to saying, "what is the probability that we would reject the null hypothesis given that it is true?")d. If you were to accept the null hypothesis, even though the null hypothesis was false, what type of error would you have commited?
A new-car dealer is leasing various brand-new models for the monthly rates(in dollars) listed below. Estimate the true population variance and standard deviation in leasing rate with 90% confidence.
Test against the null hypothesis of a one sided alternative that the difference is more than 10 minutes. Use a .1 level of significance (alpha).
Estimate with 95% confidence the mean reduction in time it takes for someone who has taken the sleeping pill to fall asleep.
One definition of a low-mileage car is one that is 4 years old and has been driven less than 45,000 miles. What percent of the cars returned are considered low-mileage?
A combination of content and supportive examples would be greatly appreciated.
Computed and shown to exceed the critical value for this data. The data is double checked and verified. This shows that car wrecks cause ice cream sales.
Explain the strength of relationship between the assets?
A biologist estimates that 40% of deer in the region carry a certain type of tick. For a sample of 300 deer selectetd at random, what is the chance that 124 or fewer deer have this tick?
A statistics profressor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 60.0 minutes. Find the probability that a given class period runs great than 50.5 minutes.
Set up a hypothesis test. Is Charmers' truthful? Describe by working through hypothesis test.
A snack company distributes chips in bags labeled 6 ounces. The local Bureau of Weights and Measures randomly selects 50 bags of chips and obtains a sample mean of 5.9 ounces.
What is the value of the slope of the least squares regression line for these data? Round your answer to at least four decimal places.
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