Question

Much concern has been expressed regarding the practice of using nitrates as meat preservatives. In one study involving possible effects of these chemicals, bacteria cultures were grown in a medium containing nitrates. The rate of uptake of radio-labeled amino acid (in dpm, disintegrations per minute) was then determined for each culture, yielding the following observations.

7256	6876	9633	6861	9094	5845	8959	7972
7064	7494	7888	8172	7524	8724	7462

Suppose that it is known that the mean rate of uptake for cultures without nitrates is 8000.

Do the data suggest that the addition of nitrates results in a decrease in the mean rate of uptake? Test the appropriate hypotheses using a significance level of 0.10. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t

=

Answer 1

Solution-

Appropriate hypotheses would be -

H₀ : $\mu$ = 8000

H_a : $\mu$ < 8000

Sample mean is calculated to be $\overline{X}$ = 7788.267 sample standard deviation (s) = 1003.004 and sample size (n) =15

then observed value of test statistic is equal to

$\frac{\overline{X}-\mu }{\frac{s}{\sqrt{n}}}$

= -0.8176

P-value will be calculated as P ( Z < - 0.8176 )

= 0.207 ( using z tables )

We use t-distribution here as sample size is not large enough ( less than 30 ).

At 10% level of significance , we compare p-value and 0.10 ( It is a one- tailed test )

As p-value > 0.10 hence null hypothesis is not rejected at 10% level of significance.

Thus we do not reject the null hypothesis and there is sufficient evidence that the the addition of nitrates does not result in a decrease in the mean rate of uptake

TY!