Perform the appropriate test of hypothesis to determine whether the new bulb should be used. Use a 0.01 level of significance
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A new light bulb is being considered for use in an office. It is decided that the new bulb will be used only if it has a mean lifetime of more than 500 hours. A random sample of 40 bulbs is selected and placed on life test. The mean and standard deviation are found to be 505 hours and 18 hours, respectively. Perform the appropriate test of hypothesis to determine whether the new bulb should be used. Use a 0.01 level of significance .
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- Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 37 randomly selected people who train in groups, and finds that they run a mean of 47.7 miles per week. Assume that the population standard deviation for group runners is known to be 3.3 miles per week. She also interviews a random sample of 49 people who train on their own and finds that they run a mean of 49.4 miles per week. Assume that the population standard deviation for people who run by themselves is 4.4 miles per week. Test the claim at the 0.10 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.Daily Driving The average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of 25 drivers over the age of 60 and finds that the mean number of miles driven is 23.4. The population standard deviation is 4.1 miles. At a = 0.01, is there sufficient evidence that those drivers over 60 years old drive less than 24 miles per day on average? Assume that the variable is normally distributed. Use the critical value method with tables. Part 1 of 5 State the hypotheses and identify the claim with the correct hypothesis. H: u = 24 not claim Η: μ 24 claim The hypothesis test is a one-tailed test. Part: 1/5 Part 2 of 5 Find the critical value(s). Round the answer to at least two decimal places. If there is more than one critical value, separate them with commas. Critical value(s):Daily Driving The average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of 25 drivers over the age of 60 and finds that the mean number of miles driven is 22.5. The population standard deviation is 4.1 miles. At a = 0.01, is there sufficient evidence that those drivers over 60 years old drive less than 24 miles per day on average? Assume that the variable is normally distributed. Use the P-value method with a graphing calculator. Part: 0 / 4 Part 1 of 4 (a) State the hypotheses and identify the claim. H,: (Choose one) ▼ OStudents preparing for comprehensive exams usually spend many hours studying. Suppose it is known that the time students spend studying for comprehensive exams has a distribution that is skewed heavily to the right with a mean of 41.3 hours and a standard deviation of 6.8 hours. If a simple random sample of 72 students is selected and the amount of time each spent studying for the comprehensive exam is determined. State and check the two assumptions.Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.A random sample of 47 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $17.51 per car. The population standard deviation is $6.05. Estimate the mean bill for all cars from the drive thru with 91% confidence.An industrial engineer is conducting a time study for a work element. The select time is 4.5 minutes, and the sample standard deviation of the observed time is 20 seconds. What is the appropriate sample size if the estimate is to be 5 percent of the true average time 95 percent of the time?According to the Statistical Abstract of the United States, the mean family size in 2010 was 3.14 persons. Suppose a random sample of 225 families taken this year yields a sample mean size of 3.05 persons, and suppose we assume the population standard deviation of family sizes is o = 1 person. Using a 5% significance level, test the hypothesis that the mean family size has decreased since 2010. Perform your hypothesis test, and select the best interpretation of your results from the choices below. Select one: O a. At the 5% level of significance the data are statistically significant. We cannot determine the average family size has decreased since 2010. O b. At the 5% level of significance the data are statisticall significant. We can determine the average family size has decreased since 2010. O c. At the 5% level of significance the data is not statistically significant. We cannot conclude the average family size has decreased since 2010. O d. At the 5% level of significance the data…Daily Driving The average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of 25 drivers over the age of 60 and finds that the mean number of miles driven is 23.4. The population standard deviation is 4.1 miles. At a = 0.01, is there sufficient evidence that those drivers over 60 years old drive less than 24 miles per day on average? Assume that the variable is normally distributed. Use the critical value method with tables. Part: 0 / 5 Part 1 of 5 State the hypotheses and identify the claim with the correct hypothesis. Ho: (Choose one) ORhys is a quality control manager at a facility that manufactures snack foods. He is interested in the number of whole mini- pretzels that are in the 10 oz bags in the latest lot produced. Rhys selects 24 bags of mini-pretzels at random from the latest lot and counts the number of pretzels in each bag His sample has a mean of 158 pretzels with a standard deviation of 1.6 pretzels. What is the margin of error with 95% confidence (2 = 2.07)? O 0.02 O 66.76 O 0.68 O 6.34An electrical firm manufacturer produces light bulbs that have different wattage for various types of usage. The distribution length of life for the light bulbs is highly skewed with many short lifetime periods. Assume that the standard deviation for this population is 25 hours. As an engineer, you want to estimate the mean lifespan of a particular light bulb. i. Determine the standard deviation of the average lifespan if 50 samples of a light bulb are taken from this population.ii. Explain why it is acceptable to assume that the mean lifespan is approximately Normal even though the population distribution is highly skewed?iii. Suppose a previous sample of 50 bulbs were selected randomly and found to have an average of 120 hours. Let u be the population mean of life lengths of all bulbs manufactured by this firm. Produce the 90% confidence interval of the mean lifespan of a certain light bulbs.iv. If the confidence level of the mean lifespan of the light bulb is higher than 90%,…The weight of trucks traveling on a particular section of Highway 2H has a population mean of 15.8 tons and a population standard deviation of 4.2 tons. What is the probability a state highway inspector could select a sample of 51 trucks and find the sample mean to be 14.3 tons or less?Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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