Question

(2 points) When a poultry farmer uses his regular feed, the newborn chickens have normally distributed weights with a mean of 61.3 oz. In an experiment with an enriched feed mixture, ten chickens are born with the following weights (in ounces). 61.5, 64.4, 66.4, 67.7, 66.2, 65, 65.8, 64.9, 66.7, 65.3 Use the a = 0.01 significance level to test the claim that the mean weight is higher with the enriched feed. (a) The sample mean is x = (b) The sample standard deviation is s = (c) The test statistic is t = (d) The critical value is t* = (e) The conclusion is CA. There is sufficient evidence to support the claim that with the enriched feed, the mean weight is greater than 61.3. B. There is not sufficient evidence to support the claim that with the enriched feed, the mean weight is greater than 61.3.

Answer 1

a)

$\bar{x}$ = $\sum$ X / n = 65.39

b)

S = sqrt [ $\sum$ X2 - n$\bar{x}$2 / (n-1) ] = 1.6802

c)

H0: $\mu$ = 61.3

Ha: $\mu$ > 61.3

Test statistics

t = ($\bar{x}$ - $\mu$ ) / ( S / sqrt ( n) )

= ( 65.39 - 61.3) / ( 1.6802 / sqrt(10) )

= 7.70

d)

From Table,

With df of 9 and significance level of 0.01,

Critical value = 2.821

e)

Since test statistics > 2.821 , reject H0.

There is sufficient evidence to support the claim that, with the enriched fee, the mean weight

is greater than 61.3