Question

The mean mass of the puppies at five months is 4.31 kg. The masses follow the normal distribution. In an effort to increase their mass, a supplement is added to their daily meals. The subsequent masses of a sample of five-month-old puppies were (in kilograms): 4.32 4.30 4.32 4.20 4.41 4.60 4.56 4.42 4.50 4.49 a. At the 0.01 level, has the supplement increased the mean mass of the puppies? (Round the final answer to 3 decimal places. Negative answers should be indicated by a minus sign.) Value of the test statistic Reject H0 if t > . (Click to select) H0. There is (Click to select) evidence to conclude that the additive increased the mean weight of puppies. b. Determine or estimate the p-value. (Round the final answer to 4 decimal places.)

Answer 1

Solution =

We are given a data of sample size n = 10

4.32,4.30,4.32,4.20,4.41,4.60,4.56,4.42,4.50,4.49

Using this, first we find sample mean() and sample standard deviation(s).

=   

= (4.32 + 4.30.......+ 4.49)/10

= 4.412

Now ,

s=   

Using given data, find Xi - for each term.Take square for each.Then we can easily find s.

s = 0.127

Then ,

The null and alternative hypothesis are,

H0 : = 4.31 ....... null hypothesis

Ha : > 4.31 ........ Alternative hypothesis

Here, n = 10 , = 4.412 , s = 0.127

The test statistic is ,

t = X - / sn = 4.412-4.31/0.127*10

= 2.54

Then, df = n - 1 = 9

> sign in Ha ====== Right tailed test

Using , t = 2.54 , df = 9 , right tailed test

P-value = 0.0159