Question

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A medical laboratory claims that the mean turn-around time for performance of a battery of tests on blood samples is 1.98 business days. The manager of a large medical practice believes that the actual mean is larger. A random sample of 45 blood samples yielded mean 2.05 and sample standard deviation 0.13 day. Perform the relevant test at the 10% level of significance, using these data.

State the null and alternative hypotheses: Ho: H1: This is a _________ test and the claim is the_________ (null or alternative hypothesis).For this study, we should use a_________ (right, left, or two-tailed) .The p-value is:_________(round to four decimal places). Because P_________0.10 we_________the null hypothesis. Thus,_________.

Answer 1

Solution :

Given that,

Population mean = = 1.98

Sample mean = = 2.05

Sample standard deviation = s = 0.13

Sample size = n = 45

Level of significance = = 0.10

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 1.98

Ha: 1.98

The test statistics,

t = ( - )/ (s/)

= ( 2.05 - 1.98 ) / ( 0.13 /45 )

= 3.612

P- Value = 0.0008

The p-value is p = 0.0008 < 0.10, it is concluded that the null hypothesis is rejected.

We reject the null hypothesis. Thus the claim is different than 1.98, at 0.10 level of significance.