8! **Crash Test Analysis of Child Booster Seats**A safety administration conducted crash tests of child booster seats for cars. The results, measured in hic (head injury criterion units), are as follows: 807, 754, 1332, 673, 598, 582. The safety standard is that the hic measurement should be less than 1000 hic.Using a significance level of 0.05, we will test the claim that the sample is from a population with a mean less than 1000 hic.Refer to section 10.1 to see examples of using t-distribution to find the P-value.**Hypothesis Testing:**1. **State the Null and Alternative Hypotheses:** - **\( H_0 \):** The population mean is equal to 1000 hic (\( \mu = 1000 \)). - **\( H_a \):** The population mean is less than 1000 hic (\( \mu < 1000 \)).2. **Find the P-value:** - Use a t-distribution to calculate the P-value. - **P-value =** __________3. **Make Your Conclusion:** - Based on the P-value, determine whether to reject or fail to reject the null hypothesis.

Given data : 807,754,1332,673,598,582 Population mean(μ0) = 1000 hic level of significance(α) = 0.05 To test the t-test, we have to find sample mean and standard deviation for given data as below, Sample mean(X)= ∑i=1nXin = 47466 = 791 Sample standard deviation(s) = 1n-1∑i=1n(Xi-X )2 = 16-1[(807-791)2+(754-791)2+(1332-791)2......+(582-791)2 = 77832 = 278.9839 Calculation : Now we use t-distribution to find P-value Null hypothesis(H0) : μ0 ≥ 1000 Alternative hypothesis(H1) : μ0 < 1000 t-statistic = x¯-μ0s/n = 791-1000278.984/6 =-209×6278.984= -209×2.4494278.984= 511.9246278.984= -1.8350 P value from t-statistic = 0.1260 .......................from t table here, P-value > 0.05 We do not reject H0 , Therefore, This result is not statistically significant Conclusion: The sample is from a population with a mean is greater than or equal to 1000 hic .