Question

8. A study of organic grown produce showed that 40 out of 400 samples had the presence of E. coli. The researchers are interested in testing whether the proportion of E. Coli in organic food (p) is lower than that from conventionally grown food which is considered to be 13%. Use the p-value approach to test the hypothesis that H0: p < 0.13 vs. HA: p > 0.13 at a significance level of α = 0.05.




9. The U.S. Department of Transportation provides the number of miles that residents of the 75 largest metropolitan areas travel per day in a car. Suppose that for a simple random sample of 60 Houston residents the mean is 25.5 miles a day and the standard deviation is 7.9 miles a day, and for an independent simple random sample of 35 Seattle residents the mean is 21.1 miles a day and the standard deviation is 8.9 miles a day. Formulate a hypothesis to test whether the difference in the mean distance travel per day is the same between Houston and Seattle. That is, test the following null hypothesis at the 5% significance level (hint: degrees of freedom = 92 :

Answer 1

Answer 8

we have population proportion po = 0.13

sample proportion

sample size n = 400

Calculation for test statistic z

z =

setting the given values, we get

z =

now, we need to find the probability of

using the identity

we can write as

using the standard normal distribution table, we get = 0.9625

So, calculated p value is greater than 0.05, this means result is insignificant and we failed to reject the null hypothesis.

We can conclude that there is enoughe evidence to warrant the rejection of claim that the proportion of E coli in organic food is greater than 13% and accept that the proportion is lower than 13%