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It is known that the thread life of a certain type of tire has a normal...

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Basic Math

It is known that the thread life of a certain type of tire has anormal distribution with standard deviation of 1500.

a) A sample of 16 tires is found to have an average thread lifeof 30960. Does this provide sufficient evidence at 1% level ofsignificance to conclude that the true average thread life of thistype of tires is more than 30000? Explain by carrying out anappropriate hypothesis test stating clearly the hypotheses.

b) What is the probability of making a Type II error in thehypothesis test in part "a" if the true average thread life is infact 31000?

c) If a 1% level of significance is used to carry out the testin part "a" and it is also required that ?(30500) = 0.05, whatsample size is necessary?

THE ANSWERS ARE AS FOLLOWS

a) ?=30000, ?>30000, z=2.56, z0.01=2.327, reject.

b) 0.3671

c) 142

Please explain the process to solve this problem. Thankyou!?

Answer & Explanation Solved by verified expert
4.1 Ratings (435 Votes)
aHypotheses areGiven informationSince population standard deviation is known so single sample ztest    See Answer
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