The average gasoline price of one of the major oil companies has been $2.40 per gallon. Because of cost reduction measures, it is believed that there has been a significant reduction in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $2.31. Assume that the standard deviation of the population (?) is $0.17. (a) State the null and the alternative hypotheses (in dollars). (Enter != for ≠ as needed.) H0:       Ha:       (b) Compute the test statistic. (Round your answer to two decimal places.)   (c) What is the p-value associated with the above sample results? (Round your answer to four decimal places.) p-value =  (d) Using ? = 0.05, test the company's claim. Do not reject H0. There is sufficient evidence that the average price has been reduced.Reject H0. There is sufficient evidence that the average price has been reduced.    Reject H0. There is insufficient evidence that the average price has been reduced.Do not reject H0. There is insufficient evidence that the average price has been reduced.

For a data set of the pulse rates for a sample of adult​ females, the lowest pulse rate is 38 beats per​ minute, the mean of the listed pulse rates is x=79.0 beats per​ minute, and their standard deviation is s=22.1 beats per minute.   a. What is the difference between the pulse rate of 38 beats per minute and the mean pulse rate of the​ females? b. How many standard deviations is that​ [the difference found in part​ (a)]? c. Convert the pulse rate of 38 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between −2 and 2 to be neither significantly low nor significantly​ high, is the pulse rate of 38 beats per minute​ significant?

In nutrition, the recommended daily allowance of vitamins is a number set by the government to guide an individual's daily vitamin intake. Actually, vitamin needs vary drastically from person to person, but the needs are closely approximated by a normal curve. To calculate the recommended daily allowance, the government first finds the standard deviation and the average need for vitamins among people in the population. The recommended daily allowance is then defined as the mean plus 2.7 times the standard deviation. What fraction of the population will receive adequate amounts of vitamins under this plan? Click here to see page 1 of the table for areas under the standard normal curve. Click here to see page 2 of the table for areas under the standard normal curve. The fraction of the population that will receive adequate amounts of vitamins under the given plan is (Type an integer or decimal rounded to the nearest thousandth as needed.)

If the mean of a data set is 12.3 and the standard deviation is 0, then a. all the observations are equal to 12.3 b. there must have been a mistake in the calculation, as it is not possible to have a standard deviation of 0 c. a histogram of the data set has a single peak at zero d. a histogram of the data set will be strongly skewed e. there is a large amount of variabitilty in the data set

Suppose there is a city where the mean cost per month of a one-bedroom apartment is $1,500, with a standard deviation of $250. Approximately what percentage of one-bedroom apartments in the city cost between $750 and $1,000?

2. The average gasoline price of one of the major oil companies has been $1.00 per gallon. Because of shortages in production of crude oil, it is believed that there has been a significant increase in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $1.04. Assume that the standard deviation of the population (o) is $0.12. a) State the null and the alternative hypotheses for testing the belief. b) Describe a Type I error and a Type II error for this situation. c) What is the critical value at a = .05? d) what's your What is the t-statistic or z-statistic associated with the above sample results?

You want to buy a washing​ machine, and a salesperson tells you that the mean repair costs for Model A and Model B are equal. You research the repair costs. The mean repair cost of 24 Model A washing machines is ​$209. Assume the population standard deviation is ​$20. The mean repair cost of 27 Model B washing machines is ​$215. Assume the population standard deviation is ​$24. At α=0.01, can you reject the​ salesperson's claim? Assume the samples are random and​ independent, and the populations are normally distributed. Complete parts​ (a) through​ (e). ​(a) Identify the claim and state H0 and Ha.   What is the​ claim?     A. The mean repair costs for Model A and Model B are equal.   B. The mean repair cost for Model A is greater than Model B.   C. The mean repair costs for Model A and Model B are different.   D. The mean repair cost for Model A is less than Model B. Let μ1 be the mean repair cost for Model A and let μ2 be the mean repair cost for Model B.…

In a large section of a statistics​ class, the points for the final exam are normally​ distributed, with a mean of 69 and a standard deviation of 9.Grades are assigned such that the top​ 10% receive​ A's, the next​ 20% received​ B's, the middle​ 40% receive​ C's, the next​ 20% receive​ D's, and the bottom​ 10% receive​ F's. Find the lowest score on the final exam that would qualify a student for an​ A, a​ B, a​ C, and a D