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erastovalidia [21]
3 years ago
7

Listed below are the lead concentrations in mu ??g/g measured in different traditional medicines. Use a 0.10 0.10 significance l

evel to test the claim that the mean lead concentration for all such medicines is less than 17 17 mu ??g/g. 6.5 18.5?21.5?5.5?8.5?4.5?4.5?17.5 15.5 20
What are the null and alternative? hypotheses?

A. Upper H0?: mu ? =17 mu ??g/g Upper H1?: mu ? ? 17 mu ??g/g

B. Upper H0?: mu > 17 mu ??g/g Upper H1?: mu ? < 17 mu ??g/g

C. Upper H0?: mu ? = 17 mu ??g/g Upper H1?: mu ? < 17 mu ??g/g

D. Upper H0?: mu ? = 17 mu ??g/g Upper H1?: mu ? > 17 mu ??g/g

Determine the test statistic. nothing ?(Round to two decimal places as? needed.)

Determine the? P-value. nothing ?(Round to three decimal places as? needed.)

State the final conclusion that addresses the original claim. ? Fail to reject Reject Upper H 0 H0. There is ? sufficient not sufficient evidence to conclude that the mean lead concentration for all such medicines is ? less than equal to greater than not 17 17 mu ??g/g.
Mathematics
1 answer:
laiz [17]3 years ago
7 0

Answer:

We conclude that the mean lead concentration for all such medicines is less than 17 mu.

Step-by-step explanation:

We are given below are the lead concentrations in mu;

6.5 18.5 21.5 5.5 8.5 4.5 4.5 17.5 15.5 20

We have to test the claim that the mean lead concentration for all such medicines is less than 17 mu.

<u><em>Let </em></u>\mu<u><em> = mean lead concentration for all such medicines.</em></u>

So, Null Hypothesis, H_0 : \mu = 17 mu      {means that mean lead concentration for all such medicines is equal to 17 mu}

Alternate Hypothesis, H_A : \mu < 17 mu       {means that the mean lead concentration for all such medicines is less than 17 mu}

The test statistics that would be used here <u>One-sample t test</u> <u>statistics</u> as we don't know about population standard deviation;

                      T.S. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}  ~ t_n_-_1

where, \bar X = sample mean lead concentration = \frac{\sum X}{n} = 12.25 mu

             s = sample standard deviation = \sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} } = 6.96 mu

             n = sample size = 10

So, <u><em>test statistics</em></u>  =  \frac{12.25 -17}{\frac{6.96}{\sqrt{10}}}  ~ t_9

                              =  -2.16

The value of t test statistics is -2.16.

<u>Now, the P-value of the test statistics is given by the following formula;</u>

                P-value = P( t_9 < -2.16) = <u>0.031</u>

<u><em>Now, at 0.10 significance level the t table gives critical value of -1.383 for left-tailed test.</em></u><em> Since our test statistics is less than the critical value of t as -2.16 < -1.383, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><em><u>we reject our null hypothesis</u></em><em>.</em>

Therefore, we conclude that the mean lead concentration for all such medicines is less than 17 mu.

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