Question

In: Statistics and Probability

ABC smoke detector manufacturer claims their smoke detectors can last with average of 105 months and...

ABC smoke detector manufacturer claims their smoke detectors can last with average of 105 months and standard deviation is 10 months. A consumer agency wants to test if the smoke detectors cannot last 105 months. A sample of 36 smoke detectors were tested with the mean of 100 months. Use the 5 percent level of significance, can the consumer agency proof the smoke detectors cannot last 105 mouths

Solutions

Expert Solution

Solution :

Givan that

= 105

= 100

= 10

n = 36

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 105

Ha :    105

Test statistic = z

= ( - ) / / n

= ( 100 - 105 ) / 10 / 36

= -3

The test statistic = -3

P - value = 2 * P (Z < -3 )

= 2 * 0.0013

= 0.0026

P-value = 0.0026

= 0.05  

0.0026 < 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to claim

Solution :


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