The quality- control manager at a light emitting diode (LED) factory needs to determine whether the mean life of a large shipment of LEDs is equal to 50,000 hours. The population standard deviation is 1,500 hours. A random sample of 64 LEDs indicates a sample mean life of 49,875 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 50,000 hours? b. Compute the p -value and interpret its meaning. c. Construct a 95 % confidence interval estimate of the population mean life of the LEDs. d. Compare the results of (a) and (c). What conclusions do you reach?
The quality- control manager at a light emitting diode (LED) factory needs to determine whether the mean life of a large shipment of LEDs is equal to 50,000 hours. The population standard deviation is 1,500 hours. A random sample of 64 LEDs indicates a sample mean life of 49,875 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 50,000 hours? b. Compute the p -value and interpret its meaning. c. Construct a 95 % confidence interval estimate of the population mean life of the LEDs. d. Compare the results of (a) and (c). What conclusions do you reach?
The quality- control manager at a light emitting diode (LED) factory needs to determine whether the mean life of a large shipment of LEDs is equal to 50,000 hours. The population standard deviation is 1,500 hours. A random sample of 64 LEDs indicates a sample mean life of 49,875 hours.
a. At the 0.05 level of significance, is there evidence that the mean life is different from 50,000 hours?
b. Compute the p-value and interpret its meaning.
c. Construct a
95
%
confidence interval estimate of the population mean life of the LEDs.
d. Compare the results of (a) and (c). What conclusions do you reach?
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
Please could you explain why 0.5 was added to each upper limpit of the intervals.Thanks
28. (a) Under what conditions do we say that two random variables X and Y are
independent?
(b) Demonstrate that if X and Y are independent, then it follows that E(XY) =
E(X)E(Y);
(e) Show by a counter example that the converse of (ii) is not necessarily true.
1. Let X and Y be random variables and suppose that A = F. Prove that
Z XI(A)+YI(A) is a random variable.
University Calculus: Early Transcendentals (4th Edition)
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