Math / Data & Statistics

QuestionBig babies: The National Health Statistics Reports described a study in which a sample of 322 one-year-old baby boys were weighed. Their mean weight was 25.1 pounds with standard deviation 5.3 pounds. A pediatrician claims that the mean weight of one-year-old boys is greater than 25 pounds. Do the data provide convincing evidence that the pediatrician's claim is true? Use the $\alpha=0.05$ level of significance and $P$ -value method with the (3) Critical Values for the Student's t Distribution Table.
Part: $0 / 5$ $\square$
Part 1 of 5 (a) State the appropriate null and alternate hypotheses. $\begin{array}{l} H_{0}: \square \\ H_{1}: \square \end{array}$
This hypothesis test is a (Choose one) $\nabla$ test. $\square$

Studdy Solution

STEP 1

1. We are conducting a hypothesis test for the mean weight of one-year-old boys.
2. The sample size is $n = 322$ .
3. The sample mean is $\bar{x} = 25.1$ pounds.
4. The sample standard deviation is $s = 5.3$ pounds.
5. The level of significance is $\alpha = 0.05$ .

STEP 2

1. State the null and alternative hypotheses.
2. Determine the type of test.
3. Calculate the test statistic.
4. Find the critical value and determine the rejection region.
5. Make a decision and interpret the results.

STEP 3

State the null and alternative hypotheses.
The null hypothesis ( $H_0$ ) is that the mean weight of one-year-old boys is equal to 25 pounds.
$H_0: \mu = 25$
The alternative hypothesis ( $H_1$ ) is that the mean weight of one-year-old boys is greater than 25 pounds.
$H_1: \mu > 25$

STEP 4

Determine the type of test.
Since we are testing the mean with a known sample standard deviation and a relatively large sample size, we use a one-sample t-test.
This hypothesis test is a one-sample t-test.
The hypotheses are:
$\begin{array}{l} H_{0}: \mu = 25 \\ H_{1}: \mu > 25 \end{array}$
This hypothesis test is a one-sample t-test.

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