The results that follow were obtained from an analysis of data obtained in a study to assess the relationship between percent increase in yield (Y) and base saturation (x1, pounds/acre), phosphate saturation (x2, BEC%), and soil pH (x3). Fifteen responses were analyzed in the study. The least-squares equation and other useful information follow. y^=38.83-0.0092x1-0.92x2-11.56x3, Syy=10965.46, SSE=1107.01

a. Is there sufficient evidence that, with all independent variables in the model, β2 < 0? Test at the α = .05 level of significance.
b. Give a 95% confidence interval for the mean percent increase in yield if x1 = 914, x2 = 65 and x3 = 6.

a. yes there is enough evidence

B. -22.83, 102.79

Step-by-step explanation:

H0: B2 >= 0

H1: B2 < 0

Alpha = 0.05

T critical is calculated to be -1.79

If t is less than -1.79 we reject the null hypothesis

Test statistic

S = √1107.01/15-3-1

= 10.032

T stat = -0.92 - 0/10.032√0.00081

= -3.222

-3.222 is less than -1.79

So we Reject the null hypothesis and conclude that enough evidence exists that B2<0

B. At 95% confidence

38.83 - 0.0092x1 - 0.92x2 + 11.56x3

= 38.83 - 0.0092x914 - 0.92x65 + 11.56x6

= 38.83 - 8.4088 - 59.8 + 69.36

= 39.98

39.98-2.2*28.55,39.85+2.2*28.55

= 39.98 - 62.81, 39.98 + 62.81

= -22.83, 102.79

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

a

step-by-step explanation:

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