Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.4 parts/million (pp

Question

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.4 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 23 samples is 4.2 ppm with a standard deviation of 0.7. Does the data support the claim at the 0.01 level? Assume the population distribution is approximately normal. Step 1 of 5: State the null and alternative hypotheses.

in progress 0
Kiệt Gia 4 years 2021-08-21T21:26:48+00:00 1 Answers 8 views 0

Answers ( )

  1. ThanhThu
    0
    2021-08-21T21:27:51+00:00
    Reply

    Solution:

    To test the hypothesis is that the mean ozone level is different from 4.40 parts per million at 1% of significance level.

    The null hypothesis and the alternative hypothesis is :

    $H_0: \mu = 4.40$

    $H_a: \mu \neq 4.40$

    The z-test statistics is :

    $z=\frac{\overline x - \mu}{\left( \sigma / \sqrt n \right)} $

    $z=\frac{4.2 - 4.4}{\left(0.7 / \sqrt{23} \right)} $

    $z =\frac{-0.2}{0.145}$

    z = -1.37

    The z critical value for the two tailed test at 99% confidence level is from the standard normal table, he z critical value for a two tailed at 99% confidence is 2.57

    So the z critical value for a two tailed test at 99% confidence is ± 2.57

    Conclusion :

    The z values corresponding to the sample statistics falls in the critical region, so the null hypothesis is to be rejected at 1% level of significance. There is a sufficient evidence to indicate that the mean ozone level is different from 4.4 parts per million. The result is statistically significant.

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )