a-e show all work please. thank you! For each of the following problems, please

Question

a-e show all work please. thank you!

For each of the following problems, please provide the requested information. (a) State the null and alternate hypotheses and the level of significance. Is the test left-tailed, righ-tailed, or he test left-tailed, right-tailed, or two-tailed? (b) Identify the appropriate sampling distribution: the standard normal or the Student's t. What is the value of the sample test statistic? (c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P. value. (d) Find the critical value(s). (e) Based on your answers for parts (a) through (d), will you reject or fail to reject the null hypothesis? Interpret your conclusion in the context of the application. 7. How big are tomatoes? Some say that depends on the growing conditions. A random sample of n 89 ically grown tomatoes had a sample mean weight of xi = 3.8 ounces. Another random sample of organically grown tomatoes had a sample mean weight of 2 75 tomato studies show that q-09 ounce and 2 = 1.5 ounces. Does this indicate that there is a difference between population mean weights of organically grown tomatoes compared to those not organically grown? Use a 5% level of significance es that were not organically grown had a sample mean weight 324.1 ounces. Previous 7. (a)

Explanation / Answer

a) H0:mu1-mu2=0 (There is no difference in mean weight of organically grown and non organically grown tomatoes)

H1:mu1-mu2 not eqaul to 0 (There is difference in mean weight of organically grown and non organically grown tomatoes).

Test is two-tailed.

b) Population standard deviations of two types of tomatoes being known, the sampling distribution is standard normal.

c) Pooled standard deviation:

sigmaXbar-Xbar=sqrt [sigma1^2/n1+sigma2^2/n2]

=sqrt[0.9^2/89+1.5^2/75]

=0.20

Z(obtained)=(X1bar-X2bar)/sigmaXbar-Xbar

=(3.8-4.1)/0.20

=-1.5

c) The p value is 0.1336.

d) For alpha=0.05, the critical Z is +-1.96 (two-tailed).

e) The test statistic do not fall in critical region, therefore, fail to reject H0, there is not sufficient sample evidence to cocnclude that there is difference in mean weight of organically grown and non organically grown tomatoes

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