Question

Probler 3 Problem 4 Problem 5 Problem 6 (8 points) A lectronics manufacturer has developed a new type of remote control button that is designed to operate longer before failing to work consistently. A random sample of 17 of the new buttons is selected and each is tested in continuous operation until it fails to work consistently. The resulting lifetimes are found to have a sample mean of x = 1245.6 hours and a sample standard deviation of 114.4. Independent tests reveal that the mean lifetime of the best remote control button on the market is 1205 hours. Conduct a hypothesis test to determine if the new button's mean lifetime exceeds 1205 hours. Round all calculated answers to four decimal places. 1. The null hypothesis is HON =1205. What is the alternate hypothesis? Problem 7 OA. HA 1205 OBHAM > 1205 C. HAN> 1245.6 OD. HAN <1205 OE HAN=1245.6 2. Which of the following conditions must be met to perform this hypoth Select all the correct answers. A. The sample must be large enough so that at least 10 buttons fail and 10 succeed. B. We must be able to expect that at least 5 buttons will fail to work consistently OC. The observations must be independent. D. The number of remote control buttons tested must be normally distributed OE. The lifetime of remote control buttons must be normally distri ibuted 3. Calculate the test statistic ? 4. Calculate the p-value 5. Calculate the effect size, Cohen's d, for this te 6. The results of this test indicate we have a... A. large B. small to moderate C. small OD moderate to large effect size, and... A. some evidence B. very strong evidence OC. extremely strong evidence OD. strong evidence E. little evidence that the null model is not compatible with our observed result

Answer 1

Given
X bar	1245.6
μ0	1205
S	114.4
n	17

1)

Ha: µ > 1205

2)

C. The observations must be independent. E. The lifetime of remote control buttons must be normally distributed

3)

Hypothesis :		α=	0.05(Let)
		df	16	n-1
Ho:	μ1 = μ0
Ha:	μ1 > μ0	right tailed
3)Test :
t	1.463270003	(X bar-μ )/(S/SQRT(n))
4)P value :
P value	0.081380615	T.DIST.RT(ts,df)	RIGHT
Decision :
P value	>	α	Do not reject

5)

cohen's d = (X bar-μ )/S = (1245.6 - 1205)/114.4 = 0.3549

6)

we have small effect size and little evidence that the null model is not compatible with our observed result