Kudzu is a plant that was imported to the United States from

Kudzu is a plant that was imported to the United States from Japan and now covers over seven million acres in the South. The plant contains chemicals called isoflavones that have been shown to have beneficial effects on bones. One study used three groups of rats to compare a control group with rats that were fed either a low dose or a high dose of isoflavones from kudzu. One of the outcomes examined was the bone mineral density in the femur (in grams per square centimeter). Researchers would like to test if the mean bone mineral density is different for the three different groups. Using the data set BoneMineralData, conduct an ANOVA test to determine if there is a difference in the means of the 3 groups. Use a level of significance of . Use this information to answer questions 1 through 5.

Kudzu is a plant that was imported to the United States from Japan and now covers over seven million acres in the South. The plant contains chemicals called isoflavones that have been shown to have beneficial effects on bones. One study used three groups of rats to compare a control group with rats that were fed either a low dose or a high dose of isoflavones from kudzu. One of the outcomes examined was the bone mineral density in the femur (in grams per square centimeter). Researchers would like to test if the mean bone mineral density is different for the three different groups. Using the data set BoneMineralData, conduct an ANOVA test to determine if there is a difference in the means of the 3 groups. Use a level of significance of n is sufficiently large. bar x will be approximately normal if n is sufficiently large. There are limits to how accurate we can measure the center of a distribution. The distribution of mu, if bar x will be close to t-confidence interval 9. Suppose you create a 95% confidence interval for a mean, and get (-2.346, 8.775). You\'ve been told to report this by saying, \'\'We are 95% confident that the true mean is between -2.346 and 8.775.\'\' Exactly what does this mean? There is a 95% chance that the true mean is between -2.346 and 8.775. 95% of all 95% confidence intervals actually contain the true mean. 95% of the data are between -2.346 and 8.775. 95% of the sample means are between -2.346 and 8.775. 10. Which one of the following is a correct statement of the Central Limit Theorem? The Central Limit Theorem is only applicable in hypothesis testing. t-confidence interval Two sample t-confidence interval Paired-samples z-confidence interval One sample 8. A salesman for a shoe company claimed runners would run faster races if they wore the company\'s brand of running shoe. A track coach wanted to see how much faster his runners would run, if they wore the company\'s shoes. He randomly selected 8 runners and had each of them run the 100-yard dash, twice. They wore their usual shoes to run the race on one day, and they wore the company\'s shoe to run the race on another day. Their times for both races were recorded, and the coach randomly selected the day each runner would wear the company\'s brand of shoe. Which confidence interval would be most appropriate for this study? One sample and 4. Give the P-value for this test. Round your answer to three decimal places (Example: 0.032) 5. Based on the decision rule, what do you conclude? Fail to reject the null. There is sufficient evidence to suggest that there is a difference in the means of one or more of the groups from the others. Fail to reject the null. There is insufficient evidence to suggest that there is a difference in the means of one or more of the groups from the others. Reject the null. There is sufficient evidence to suggest that there is a difference in the means of one or more of the groups from the others. Reject the null. There is insufficient evidence to suggest that there is a difference in the means of one or more of the groups from the others. 6. A real estate company wants to evaluate two of their home appraisers for consistency in preparation for their annual state certification. It is important that different appraisers be able to give similar estimates for homes and other properties. The company selects a random sample of 10 homes in different neighborhoods around the city and independently asks each appraiser for an estimate of the home value. After they receive the estimates for each home, the company subtracts the value given by the first appraiser from the value given by the second appraiser. They create a Q-Q plot of the differences and see that the points in the plot roughly form a straight line. Are the requirements for using the desired confidence interval satisfied? Explain. Yes. The distribution of mean differences is normal because the sample size is large. Yes. The distribution of mean differences is normal because the data have been determined to be normal. No. The distribution of mean differences is not normal because the sample size is not large enough. Not necessarily, because the company needs to check that the values given by each appraiser are normal, not that the differences are normal. 7. Now suppose the company of the previous item wants to use a hypothesis test to determine whether the estimates given by the two appraisers are different. Which of the following would be the most appropriate pair of hypotheses for such a test? F = text (Two or more of the means are not equal to the others) 2. Check that the requirements for this data are met. Check that data are normally distributed in each group and that the variances are equal for each group. Which of the following statements is true? The data are approximately normal for each group, the variances are equal for each group The data are clearly not normal for each group, the variances are equal for each group The data are approximately normal for each group, the variances are not equal for each group The data are clearly not normal for each group, the variances are not equal for each group. If the requirements from Question 2 were not satisfied, conduct the test anyway. 3. Give the value of the test statistic and the degrees of freedom, in the appropriate order. Give the test statistic accurate to 3 decimal places. (Example: 4.567) H_a: text (All the means are equal) H_o: text (One of the means is greater than the others) H_a: text (All the means are equal) H_o: text (All the means are equal) H_a: text (At least one of the means differs) H_o: text (At least one of the means differs) H_a: text(All the means are equal) H_o: alpha = 0.05 . Use this information to answer questions 1 through 5. 1. What are the null and alternative hypotheses?

Solution

The data set are

1.The null and alternative hypotheses are

H₀: All the means are equal

H_a: At least one of the means differs

2. Using the R-command, we show that the data are normal or not

control=c(0.228,0.207,0.234,0.22,0.217,0.228,0.209,0.221,0.204,0.22,0.203,0.219,0.218,0.245,0.21)
high =c(0.25,0.237,0.217,0.206,0.247,0.228,0.245,0.232,0.267,0.261,0.221,0.219,0.232,0.209,0.255)
low =c(0.211,0.22,0.211,0.233,0.219,0.233,0.226,0.228,0.216,0.225,0.2,0.208,0.198,0.208,0.203)
par(mfrow=c(3,2))
hist(control, freq = FALSE, main=\"Histogram for Control\")
curve(dnorm(x, mean=mean(control), sd=sd(control)), col=\"blue\", lwd=2,add=TRUE)
lines(density(control),col = \"red\", lwd=2)
qqnorm (control, main = \"Normal Quantile Plot for Control\")
qqline (control)
hist(low, freq = FALSE, main=\"Histogram for Low Dose\")
curve(dnorm(x, mean=mean(low), sd=sd(low)), col=\"blue\", lwd=2,add=TRUE)
lines(density(low),col = \"red\", lwd=2)
qqnorm (low, main = \"Normal Quantile Plot for Low Dose\")
qqline (low)
hist(high, freq = FALSE, main=\"Histogram for High Dose\")
curve(dnorm(x, mean=mean(high), sd=sd(high)), col=\"blue\", lwd=2,add=TRUE)
lines(density(high),col = \"red\", lwd=2)
qqnorm (high, main = \"Normal Quantile Plot for High Dose\")
qqline (high)

These graphs show that the data are approximately normal for each group, the variances are equal for each group

3. THe test statistic is find by using Excel

The F-value is 7.71823 with df 2,42

4. The p-value is 0.001397

5. Reject the null. There is sufficient evidence to suggest that there is a difference in the means of one or more of the groups from the others.

Control	Low dose	High Dose
0.228	0.211	0.25
0.207	0.22	0.237
0.234	0.211	0.217
0.22	0.233	0.206
0.217	0.219	0.247
0.228	0.233	0.228
0.209	0.226	0.245
0.221	0.228	0.232
0.204	0.216	0.267
0.22	0.225	0.261
0.203	0.2	0.221
0.219	0.208	0.219
0.218	0.198	0.232
0.245	0.208	0.209
0.21	0.203	0.255