Question

A particular species of salmon has an average weight of 57 lb, with a standard deviation of 6.3 lbs. Researchers studying salmon in a particular river find that in a sample of 45 fish, average weight is 60.2 lbs. What should researchers do?

a. Reject the null hypothesis; these fish are not larger than usual

b. Do not reject the null hypothesis; these fish are larger than usual

c. Do not reject the null hypothesis; these fish are not larger than usual

d. Reject the null hypothesis; these fish are larger than usual​

Answer 1

Explanation:

Given:

population mean, mu = 57 lb

population standard deviation, sigma = 6.3 lb

Sample mean, x = 60.2 lb

Sample size, n= 45

Null hypothesis x = mu (i.e. sample mean is not greater than usual, using a significance level of 0.05)

Here we have a case where population mean and standard deviation are known (given).

We calculate the z-score

z=(x-mu)/(sigma/sqrt(n))

= (60.2-57)/(6.3/sqrt(45))

= 3.41

P(x>mu) = P(z>3.41) = 0.99968 >> 0.95 (one sided tail)

Therefore we can reject the null hypothesis and accept the alternate hypothesis that fish are larger than usual.