Question

Heights​ (cm) and weights​ (kg) are measured for 100 randomly selected adult​ males, and range from heights of 133 to 193 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x overbarequals167.90 ​cm, y overbarequals81.47 ​kg, requals0.228​, ​P-valueequals0.023​, and ModifyingAbove y with caretequalsnegative 105plus1.13x. Find the best predicted value of ModifyingAbove y with caret ​(weight) given an adult male who is 172 cm tall. Use a 0.05 significance level. The best predicted value of ModifyingAbove y with caret for an adult male who is 172 cm tall is nothing kg. ​(Round to two decimal places as​ needed.)

Answer 1

Answer:

The weight of an adult male who is 172 cm tall is 89.36 kg.

Step-by-step explanation:

The regression equation representing the relationship between height and weight of a person is:

$\hat y=-105+1.13x$

Here

y = weight of a person

x = height of a person

The information provided is:

$\bar x=167.90\ cm\\\bar y=81.47\ kg\\r (X, Y) = 0.228\\p-value=0.023\\\alpha =0.05$

The hypothesis to test the significance of the correlation between height and weight is:

H₀: There is no relationship between the height and weight, i.e. ρ = 0.

Hₐ: There is a relationship between the height and weight, i.e. ρ ≠ 0.

Decision rule:

If the p-value of the test is less than the significance level, then the null hypothesis will be rejected and vice-versa.

According to information provided:

p-value = 0.023 < α = 0.05

The null hypothesis was rejected at 5% level of significance.

Thus, concluding that there is a relationship between the height and weight.

Compute the weight of an adult male with height, x = 172 cm as follows:

$\hat y=-105+1.13x$

  $=-105+(1.13\times 172)\\=-105+194.36\\=89.36$

Thus, the weight of an adult male who is 172 cm tall is 89.36 kg.