The Insure.com website reports that the mean annual premium for automobile insurance in the United States was $1,503 in March 2014. Being from Pennsylvania at thattime, you believed automobile insurance was cheaper there and decided to develop statistical support for your opinion. A sample of 25 automobile insurance policies from thestate of Pennsylvania showed a mean annual premium of $1,435 with a standard deviation of s= $170.(a) Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium.OH1,503H1,503OHe: >1,503H₁1,503Ho: 21,503H: <1,503Hos 1,503H> 1,503M¹ <1,503M21,503(b) What is a point estimate in doilers of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium inPennsylvania minus the national mean.)$(c) At a 0.05, test for a significant difference.Find the value of the test statistic. (Round your answer to three decimal places.)xFind the p-value. (Round your answer four decimal places)Pvalve-o

Given data is sample size(n)=25sample mean(x)=1435standard deviation(s)=170

Answered: The Insure.com website reports that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The Insure.com website reports that the mean annual premium for automobile insurance in the United States was $1,503 in March 2014. Being from Pennsylvania at that time, you believed automobile insurance was cheaper there and decided to develop statistical support for your opinion. A sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $1,430 with a standard deviation of s = $160. (a) Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual O Ho: u = 1,503 H: u # 1,503 premium. o Ho: H 1,503 O Ho: H > 1,503 Ha:uS 1,503 (b) What is a point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium in Pennsylvania minus the national mean.)
The America Automobile Association reported that the mean price of a gallon of regular grade gasoline in the United States in October 2020 was $2.82. An economist is interested in determining whether the mean price of regular grade gasoline is cheaper (less than) in New York State. To test this, the economist sample 50 gas stations in NY and find the mean price of regular grade gasoline to be $2.77. Assume the standard deviation for the price of regular grade gasoline is $0.15. Use the critical value method to perform a hypothesis test at the 0.05 level of significance. a) what is the conclusion for this test?
The America Automobile Association reported that the mean price of a gallon of regular grade gasoline in the United States in October 2020 was $2.82. An economist is interested in determining whether the mean price of regular grade gasoline is cheaper (less than) in New York State. To test this, the economist sample 50 gas stations in NY and find the mean price of regular grade gasoline to be $2.77. Assume the standard deviation for the price of regular grade gasoline is $0.15. Use the critical value method to perform a hypothesis test at the 0.05 level of significance. a. Define the parameter we are testing and setup a hypothesis test to see if the mean price of gas is cheaper in NY compared to the national mean: b. Calculate the test statistics for this hypothesis test. c.What is the critical value for this hypothesis test?
Fuel efficiency of Prius: Fueleconomy.gov, the official US government source for fuel economy information, allows users to share gas mileage information on their vehicles. The histogram below shows the distribution of gas mileage in miles per gallon (MPG) from 14 users who drive a 2012 Toyota Prius. The sample mean is 53.3 MPG and the standard deviation is 5.2 MPG. Note that these data are user estimates and since the source data cannot be verified, the accuracy of these estimates are not guaranteed. (a) The EPA claims that a 2012 Prius gets 50 MPG (city and highway mileage combined). Do these data provide strong evidence against this estimate for drivers who participate on fueleconomy.gov? The test statistic is: __________________(please round to two decimal places)The p-value:___________________________ for this hypothesis test is: (please round to four decimal places)(c) Please comment on the primary thing that is wrong about the following statement: There is sufficient evidence…
Bone mineral density (BMD) is a measure of bone strength. Studies show that BMD declines after age 45. The impact of exercise may increase BMD. A random sample of 59 women between the ages of 41 and 45 with no major health problems were studied. The women were classified into one of two groups based upon their level of exercise activity: walking women and sedentary women. The 39 women who walked regularly had a mean BMD of 5.96 with a standard deviation of 1.22. The 20 women who are sedentary had a mean BMD of 4.41 with a standard deviation of 1.02. Which of the following inference procedures could be used to estimate the difference in the mean BMD for these two types of women
According to the American Academy of Sleep Medicine, a healthy adult should obtain at least 7 hours of sleep per night. But is this happening in New York City- aka "the city that never sleeps" ? A study of 28 NYC adults chosen at random found that the sample mean was 6.73 hours and the sample standard deviation was 0.79 hours. Is there statistically significant evidence that NYC adults, on average, sleep less than 7 hours per night? Is the result "practically significant"?
According to the USDA, the mean intake of calories of males 20-39 is 2716 with a standard deviation of 72.8Would you find it unusual to have a sample mean of 2750 or higher for a sample size of 35? Why?
Suppose that a report by a leading medical organization claims that the healthy human heart beats an average of 72 times per minute. Advances in science have led some researchers to question if the healthy human heart beats an entirely different amount of time, on average, per minute. They obtain pulse rate data from a sample of 85 healthy adults and find the average number of heart beats per minute to be 76, with a standard deviation of 13. Before conducting a statistical test of significance, this outcome needs to be converted to a standard score, or a test statistic. What would that test statistic be? (Use decimal notation. Give your answer to one decimal place.) test statistic:
According to the Insurance Association in US, the average annual expenditure for automobile insurance is $605. Suppose that in a simple random sample of 80 residents of New York, for most recent year their average expenditure was $638.62 with the standard deviation of $106.05. Based on these data, examine whether the average annual insurance for motorists in New York might be different from that in national level. Using the 0.05 level of significance, what conclusion do you reach? Also, construct and interpret 95% confidence interval for the population mean. Is the hypothesized mean within the interval? Is this consistent with the findings of the hypothesis test conducted?
a Leche League International reports that the mean age of weaning a child from breastfeeding is age four to five worldwide. In America, most nursing mothers wean their children much earlier. Suppose a random survey is conducted of 21 U.S. mothers who recently weaned their children. The mean weaning age was 9 months (3/4 year) with a standard deviation of 2 months. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is less than four years old. Conduct a hypothesis test at the 5% level. a. What is the p-value? (Round your answer to four decimal places.) b. What is the test statistic
Define Test a correlation for significance?
I wanted to do a market research study estimating the average hourly wage earned by childcare workers in the bay area. How large does my sample need to be in order to have a margin of error that is less than $0.50 with a 95% confidence in the result. Assume that the standard deviation of the wages is $2 per hour.

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