Question

# Suppose that the weights of all mice are known to be normally distributed with mean µ...

Suppose that the weights of all mice are known to be normally distributed with mean µ = 30 grams and standard deviation σ = 5. You have a sample of 50 brown mice. The sample mean for your 50 brown mice is 53 grams. You believe that weights of brown mice are diﬀerent than mice in general. Suppose that the weights of brown mice are also normally distributed with known standard deviation of 5 grams.

(a) State the null and alternative hypotheses using correct mathematical notation.

(b) Calculate the test statistic z.

(c) Calculate the p-value for this test.

(d) Are these data signiﬁcant at the 95% signiﬁcance level?

(e) Interpret your p-value and state the conclusion of your hypothesis test in a complete sentence.

Given:

= 30 grams, n = 50, = 53 grams, = 5 grams, = 0.05

Hypothesis:

b)

Test statistic:

C)

P-value: 0.0000       ...................Using standard Normal table

d)

P-value < , i.e. 0.0000 < 0.05, that is Reject Ho at 5% level of significance.

e)

Therefore, there is sufficient evidence to conclude that, the weights of brown mice are different than mice in general.