Is the gestational age (time between conception and birth) of a low birth-weight baby useful in predicting head circumference at birth? Twenty-five low birth-weight babies were studied at a Harvard teaching hospital; the investigators calculated the regression of head circumference (measured in centimeters) against gestational age (measured in weeks). The estimated regression line is given below. head circumference - 3.91 + 0.78 x gestational age (a) What is the predicted head circumference for a baby whose gestational age is 33 weeks? (Enter your answer to two decimal places.) cm (b) The standard error for the coefficient of gestational age is 0.35, which is associated with df - 23. Does the model provide strong evidence that gestational age is significantly associated with head circumference? (Use a significance level of 0.05.) State the appropriate null and alternative hypotheses. O Ho: B, -0 O Hoi Bq z 0 O Hoi Bq = 0 HA: B, > 0 O Ho: Bq #0 HA: B, -0 O Hoi B, s0 Calculate the test statistic. (Round your answer to two decimal places.) T-
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In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
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![### Predicting Head Circumference of Low Birth-Weight Babies Using Gestational Age
Is the gestational age (time between conception and birth) of a low birth-weight baby useful in predicting head circumference at birth? Twenty-five low birth-weight babies were studied at a Harvard teaching hospital; the investigators calculated the regression of head circumference (measured in centimeters) against gestational age (measured in weeks). The estimated regression line is given below.
**Regression Line**:
\[ \text{head circumference} = 3.91 + 0.78 \times \text{gestational age} \]
(a) **What is the predicted head circumference for a baby whose gestational age is 33 weeks?**
(Enter your answer to two decimal places.)
\[ \text{Answer:} \quad \_\_\_\_\_\ \text{cm} \]
(b) **The standard error for the coefficient of gestational age is 0.35, which is associated with \( df = 23 \). Does the model provide strong evidence that gestational age is significantly associated with head circumference?**
(Use a significance level of 0.05.)
**State the appropriate null and alternative hypotheses**:
\[ H_0: \beta_1 = 0 \]
\[ H_1: \beta_1 \neq 0 \]
\[ H_0: \beta_1 = 0 \]
\[ H_1: \beta_1 \geq 0 \]
\[ H_0: \beta_1 = 0 \]
\[ H_1: \beta_1 \leq 0 \]
\[ H_0: \beta_1 = 0 \]
\[ H_1: \beta_1 > 0 \]
\[ H_0: \beta_1 = 0 \]
\[ H_1: \beta_1 < 0 \]
**Calculate the test statistic**.
(Round your answer to two decimal places.)
\[ T = \_\_\_\_\_\ \]
**Explanation of Diagram**:
A diagram or image shows multiple hypothesis options with radio buttons next to them, indicating the selection of the fourth option:
\[ H_0: \beta_1 = 0 \]
\[ H_1: \beta_1 > 0 \]
This option is highlighted as the selected hypothesis test for the given scenario.
### Instructions:
1. To predict the head](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde58d5f0-b651-402b-8387-7affdca0c167%2F2434ff54-8b6b-43b7-ac0f-e28d3a883937%2F97u6sw_processed.png&w=3840&q=75)
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