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- Apply Chebyshev’s rule to solve. A quantitative data set of size 60 has mean 100 and standard deviation 16. At least howmany observations lie between 68 and 132?The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,492 hours. The population standard deviation is 92 hours. A random sample of 64 light bulbs indicates a sample mean life of 7,469 hours. What is/are the critical value(s)?A supplier is selling lumber to a building supply company. The building supply company requires that the overall length of a particular type of board measure between 95.9 and 96.1 inches. Before sending its next shipment, the supplier collects a large sample of boards and determines the mean length of the sample is 96.03 inches, with a standard deviation of 0.029 inches. If the process is improved, so that its mean is equal to the target value (i.e., the process is centered), what is the potential process capability? Two decimal places.
- A contractor claims that the mean compressive strength for a concrete mix is 5000 psi (μ) and that it has a standard deviation of 400 psi (σ). If you break 20 cylinders (N) and obtain a mean compressive strength of 4,800 psi (m), would you believe the contractor’s claim? Why? (Hint; Use statistical t-test.) Next, what is the maximum number of breaks (N) that could be performed that WOULD make you believe the contractor’s claim? Assume that the results wouldn’t change, i.e. σ = 400 psi and m = 4,800 psi. Recall that the equation to find the lower bound of a one sided distribution is LB = μ - (tσ)* σ/(N^0.5) Because the sample size is relatively small, use the ‘student t test’ to represent the normal distribution. You should have at least 95% confidence in the results. That means that α = 0.05. Keep in mind that this is a one tailed distribution, since we only care about the lower bound (i.e. meaning that we are only concerned about concrete that doesn’t meet our minimum strength…A professional racing team is holding tryouts at its test track. The team requires its drivers to have an average lap time of at most 133 seconds at its test track. The team will use a one sample z-test of significance to determine if they should hire a new driver. Using the P-value you computed in the previous problem, determine if the team has significant evidence (at level 0.05) that this driver should not join the team. a. Yes, the data is significant at level 0.05, so we reject H0, which assumed the driver had the needed average lap time. b. No, the data is significant at level 0.05, so we fail to reject H0, which assumed the driver had the needed average lap time. c. No, the data is not significant at level 0.05, so we fail to reject H0, which assumed the driver had the needed average lap time. d. Yes, the data is significant at level 0.05, so reject Ha.The mean salary of federal government employees on the General Schedule is $59,593. The average salary of 30 state employees who do similar work is $58,800 with σσ= $1500. At the 0.01 level of significance, can it be concluded that state employees earn on average less than federal employees? What is the statistic value?
- To estimate a student’s average score, we need to collect a sample. Assume population standard deviation is equal to 3, If we want to control the error within 0.2 with 98% confidence level, how large the sample size need to be?A quality control expert at a local dairy claims that its cartoons contain more than 64oz of milk a sample of 15 cartoons reveals a mean of 65 and 1.1 oxs respectively. At the 1% level, does the appropriate hypothesis support his claim? find and interpret the p valueA physician claims that joggers’ maximal volume oxygen uptake is greater than the average of all adults. A sample of 15 joggers has a mean of 40.6 milliliters per kilogram (ml/kg) and a standard deviation of 6 ml/kg. If the average of all adults is 36.7 ml/kg, is there enough evidence to support the physician’s claim at α = 0.05?
- A manufacturer of bolts has a quality control policy that requires it to destroy any bolts that are more than 2 standard deviations from the mean. The quality control engineer knows that the bolts coming off the assembly line have mean length of 12 cm with a standard devation of 0.10cm. For what lengths will a bolt be destroyed?For a one-sample z-test, the population's standard deviation is ________ . Group of answer choices always equal to one not needed known not knownA sample of 50 cans of tomatoes are tested for levels of the chemical BPA to see if there is evidence that the mean level is greater than 100 ppb (parts per billion). a. Write down the hypotheses for this test (Do not forget to define the parameters): b. Give a possible sample mean that you think would show strong evidence against the null hypothesis and in support of the alternative hypothesis: