Apharmaceutical company claims that the average cold lasts an average of 8.4 days. they are using this as a basis to test new medicines designed to shorten the length of colds. a random sample of 106 people with colds, finds that on average their colds last 8.5 days. the population is normally distributed with a population standard deviation of 0.9 days. at α=0.02, what type of test is this and can you support the company’s claim using the p-value?

Let be the population mean.

Null hypothesis :

Alternative hypothesis :

Since the alternative hypothesis is left tailed, so the test is a left-tailed test.

Sample size : n=106 >30 , so we use z-test.

Test statistic:

The P-value (Left tailed test)=

Since, the p-value is greater than the significance level , so we fail to reject the null hypothesis.

Hence, we cannot support the company's claim.

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