assume that a simple random sample has been selected from a normally distributed population and test the given claim. identify the null and alternative hypotheses, test statistic, p-value, and state the final conclusion that addresses the original claim.
a safety administration conducted crash tests of child booster seats for cars. listed below are results from those tests, with the measurements given in hic (standard head injury condition units). the safety requirement is that the hic measurement should be less than 1000 hic. use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. do the results suggest that all of the child booster seats meet the specified requirement?
740 731 1225 692 597 785

what are the hypotheses?
a. \$h_0: \mu = 1000\text{ hic}\$
\$h_1: \mu < 1000\text{ hic}\$

b. \$h_0: \mu < 1000\text{ hic}\$
\$h_1: \mu \ge 1000\text{ hic}\$

c. \$h_0: \mu = 1000\text{ hic}\$
\$h_1: \mu \ge 1000\text{ hic}\$

d. \$h_0: \mu > 1000\text{ hic}\$
\$h_1: \mu < 1000\text{ hic}\$

identify the test statistic.
\$t = -2.283\$ (round to three decimal places as needed.)

identify the p-value.
the p-value is
(round to four decimal places as needed.)

Question

assume that a simple random sample has been selected from a normally distributed population and test the given claim. identify the null and alternative hypotheses, test statistic, p-value, and state the final conclusion that addresses the original claim.
a safety administration conducted crash tests of child booster seats for cars. listed below are results from those tests, with the measurements given in hic (standard head injury condition units). the safety requirement is that the hic measurement should be less than 1000 hic. use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. do the results suggest that all of the child booster seats meet the specified requirement?
740 731 1225 692 597 785

what are the hypotheses?
a. $h_0: \mu = 1000\text{ hic}$
$h_1: \mu < 1000\text{ hic}$

b. $h_0: \mu < 1000\text{ hic}$
$h_1: \mu \ge 1000\text{ hic}$

c. $h_0: \mu = 1000\text{ hic}$
$h_1: \mu \ge 1000\text{ hic}$

d. $h_0: \mu > 1000\text{ hic}$
$h_1: \mu < 1000\text{ hic}$

identify the test statistic.
$t = -2.283$ (round to three decimal places as needed.)

identify the p-value.
the p-value is
(round to four decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Hypothesis Testing", "One-Sample t-Test Statistic" ], "new_concepts": [], "current_concepts": [ "Hypothesis Testing", "One-Sample t-Test Statistic", "P-value Calculation" ] } ## Calculate sample statistics $$ \begin{aligned} &n = 6\ &\text{Data: } 740, 731, 1225, 692, 597, 785\ &\bar{x} = \frac{740 + 731 + 1225 + 692 + 597 + 785}{6} = \frac{4770}{6} = 795\ &s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}} = \sqrt{\frac{225350}{5}} = \sqrt{45070} \approx 212.29696 \end{aligned} $$ ## Compute test statistic $$ \begin{aligned} &\mu_0 = 1000\ &t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}} = \frac{795 - 1000}{212.29696 / \sqrt{6}} = \frac{-205}{86.66987} \approx -2.36529 \end{aligned} $$ ## Determine P-value $$ \begin{aligned} &df = n - 1 = 5\ &\text{Alternative hypothesis: } H_1: \mu < 1000 \quad (\text{left-tailed test})\ &P = P(T_{5} \le -2.36529) \approx 0.0321 \end{aligned} $$ Identify the P-value. The P-value is 0.0321 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "P-value Calculation" ] }

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Question

Explanation:

Calculate sample statistics

Compute test statistic

Determine P-value

Answer: