I cant seem to figure this problem out. Final tomorrow . Please help. Thanks. Re

Question

I cant seem to figure this problem out. Final tomorrow . Please help. Thanks.

Reports Magazine tested the market -leading child car-seat. They wanted to determine how safe it in car crashes of various speeds. The company conducted 36 tests, and for each test, they recorded the speed at which a problem with the car seat first appeared (broken strap, cracked casing, etc). Since the company claims the seats are completely safe in 30 mph car crashes, we want to test whether the average speed at which the seat first has problems is lower than 30 mph because this would mean that the company's claims are wrong. Therefore, the hypotheses we would test are: H_0: mu = 30mph H_a: mu 30 mph After the 36 tests, the sample average speed at which the seat had its first problem was 29.12 mph, and the sample standard deviation was 1.79 mph. What is the probability of seeing an outcome as small or smaller than 29.12 just by chance, assuming the true mean really is 30mph?

Explanation / Answer

here std error of mean =std deviation/(n)1/2 =1.79/(36)1/2 =0.2983

therefore test statistics t=(X-mean)/std error =(29.12-30)/0.2983=-2.9497

for above at (n-1=35) degree of freedom probability =0.0028

please revert for any clarification required

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