A random sample of 25,000 ACT test takers had an average score of 25 with a standard deviation of 6. Determine the standard error.
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A random sample of 25,000 ACT test takers had an average score of 25 with a standard deviation of 6. Determine the standard error.
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- The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.05 level that the medicine relieves pain in more than 365 seconds. For a sample of 47 patients, the mean time in which the medicine relieved pain was 370 seconds. Assume the population standard deviation is 25. Find the P-value of the test statistic.Provide the null and alternative hypotheses used to address these problems. Make sure that your notation is understandable.The average rainfall in a certain area is 24.5 inches per year, with a standard deviation of 3 inches per year. What is the chance they get more than 32 inches of rain next year?
- Assume that adults have IQ scores that are normally distributed with a mean of 103.1 and a standard deviation 19.6. Find the first quartile Q1, which is the IQ score separating the bottom 25% from the top 75%.The weight of potato chips in a large-size bag is stated to be 24 ounces. The amount that the packaging machine puts in these bags is believed to have a normal model with a mean of 24.2 ounces and a standard deviation of 0.12 ounces.Assume that adults have IQ scores that are normally distributed with a mean of 104.8 and a standard deviation 21.9. Find the first quartile Q1, which is the IQ score separating the bottom 25% from the top75%
- A consumer advocacy group tested the ”on-air” lifetimes of a random sample of 200 cell phone batteries. The mean lifetime was 2.7 hours with a standard deviation of 0.3 hours. The lifetimes are approximately bell-shaped. estimate the number of batteries with lifetimes between 2.4hours and 3 hours.A test was administered for a group of 400 students and scores were obtained. The scores are approximately normally distributed with a mean of 65 and standard deviation of 4.5. What are the scores within which approximately 95% of the total test scores fall?In the 1800s, German physician Carl Reinhold, took millions of axillary (i.e. armpit) temperatures from soldiers. This study established that body temperature is normally distributed and the standard normal human body temperature is 98.6°F with a standard deviation of 0.72 °F. In a recent study, American researchers obtained 5,000 axillary temperatures from a Los Angeles hospital. The mean of these temperature readings was 97.9 °F. Assuming a Type I error risk of no more than 5%, did the findings support the theory that human, body temperature has decreased since the 1800s? What is the Z crit?
- A company has developed an electric car they say can travel over 500 mues on a single charge. A consumer car magazine wants to test this claim. The magazine randomly selects 16 owners of the car and ask them to measure how far the car can travel on a full charge. The mean distance traveled by these 16 cars was 510 miles with a standard deviation of 20 miles. Test the hypothesis that the mean distance the car can travel on a single charge is greater than 500 miles. Use a 0.05 level of significance. (Assume that the distances the car can travel on one charge are normally distributed.) (a) State the null and alternative hypothesis. (b) Will this be a right-tailed, left-tailed, or two-tailed test? (c) Calculate the test statistic assuming the null hypothesis is true. T = %3D (d) Use the test statistic to calculate the P-value for the test. P- value = (e) Does the data provide enough evidence to conclude that, at the 5% significance level, the mean distance this car can travel with a full…A local community college reported that the average SAT score of its students is 960 with a standard deviation of 82. If a student scored 975 on the SAT, what is the student's z score? Did the student do better or worse on the SAT compared to the average student in the college?A study of commuting times reports the travel times to work of a random sample of 1068 employed adults in Chicago. The mean is x = 54.0 minutes and the standard deviation is s = 60.9 minutes. What is the standard error of the mean?
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