A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 758 hours. A random sample of 27 light bulbs has a mean life of 737 hours. Assume the population is normally distributed and the population standard deviation is 61 hours. At α=0.08, do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e). (a) write out the null and alternative hypotheis and the claim. (b) identify the critical value(s) use technology Z0= ___ (use a comma to seperate answers as needed. round to 2 decimal places as need) (inv in calculator) Write out a graph showing the rejection region (s). (c) identify the standardized test statistic. Use technology Z= (d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the orginal claim. A. Fail to reject Ho. There is not sufficient evidence to reject the claim that mean bulb life is at least 758 hours B. Reject Ho. There is not sufficient evidence to reject the claim that mean bulb life is at least 758 hours. C. Reject Ho. THere is sufficient evidence to reject the claim that mean bulb life is at least 758 hours. D. Fail to reject Ho. THere is sufficient evidence to reject the claim that mean bulb life is at least 758 hours.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 26PFA

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Can you please help me with a stats problem/please help with TI-84 commands,

Homework:7.2 & 7.3

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least

758

hours. A random sample of

light bulbs has a mean life of

737

hours. Assume the population is normally distributed and the population standard deviation is

hours. At

α=0.08,

do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e).

(a) write out the null and alternative hypotheis and the claim.

(b) identify the critical value(s) use technology

Z0= _________________

(use a comma to seperate answers as needed. round to 2 decimal places as need) (inv in calculator)

Write out a graph showing the rejection region (s).

Z= ______________

(d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the orginal claim.

A. Fail to reject Ho. There is not sufficient evidence to reject the claim that mean bulb life is at least 758 hours

B. Reject Ho. There is not sufficient evidence to reject the claim that mean bulb life is at least 758 hours.

C. Reject Ho. THere is sufficient evidence to reject the claim that mean bulb life is at least 758 hours.

D. Fail to reject Ho. THere is sufficient evidence to reject the claim that mean bulb life is at least 758 hours.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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