Can someone help/check with these questions. I did majority of the work. but some i need help with.

Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Suppose that Table 13.26 shows the results of a study (listed below) Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data
were collected independently and randomly. Use a level of significance of 0.05. (graph from excel is also listed below).

a. Ho

b. Ha

c. In words, CLEARLY state what your random variable X bar or P′ represents.(xbar stands for mean number of times a month a person eats out)

d. State the distribution to use for the test. ( f distribution)

e. What is the test statistic? (f statistic 0.885)

f. What is the p-value? In one or two complete sentences, explain what the p-value means for this problem. ( I know the p value is 0.471 but i don't know what it means for this problem)

g. Use the previous information to sketch a picture of this situation. CLEARLY, label and scale the horizontal axis and shade the region(s) corresponding to the p-value. (is there a sight i can do this on?)

h. Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences

Alpha: (0.05)

Decision: (do not reject h0)

Reason for decision: p value 0.471 > 0.05)

Conclusion: (?)

i. Construct a 95% confidence interval for the true mean or proportion. Include a sketch of the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval.
WHITE
6
8
2
4
6

BLACK
4
1
5
2

HISPANIC
7
3
5
4
6

ASIAN
8
3
5
1
7



SUMMARY

f = 0.885297483
p value = 0.471058044
f crit = 3.287382105
ss between groups = 13.03157895
ss within groups = 73.6

a. The null hypothesis (Ho) is that the mean number of times a month a person eats out is the same for whites, blacks, Hispanics, and Asians.

b. The alternative hypothesis (Ha) is that the mean number of times a month a person eats out is different for at least one of the ethnic groups.

c. The random variable X bar represents the mean number of times a month a person eats out.

d. The distribution to use for the test is the F-distribution.

e. The test statistic is the F-statistic, which in this case is 0.885.

f. The p-value is 0.471. The p-value represents the probability of observing a test statistic as extreme as the one calculated (or more extreme) under the assumption that the null hypothesis is true. In this problem, since the p-value is greater than the level of significance (0.05), we fail to reject the null hypothesis.

g. To sketch a picture of this situation, you can use any graphing software or even manually draw a graph. On the horizontal axis, you can label the different ethnic groups (whites, blacks, Hispanics, and Asians). On the vertical axis, you can label the mean number of times a month a person eats out. To shade the region corresponding to the p-value, you would shade the area in the tail(s) of the F-distribution curve that represents the probability equal to or more extreme than the calculated p-value.

h. The correct decision is to "do not reject" the null hypothesis. The reason for this decision is that the p-value (0.471) is greater than the level of significance (0.05). Therefore, we do not have enough evidence to conclude that there is a difference in the mean number of times a month a person eats out among the ethnic groups.

Conclusion: Based on the results of the hypothesis test, we do not have sufficient evidence to conclude that there is a significant difference in the mean number of times a month a person eats out among whites, blacks, Hispanics, and Asians.

i. To construct a 95% confidence interval for the true mean, you would use the formula:

CI = x-bar ± (t * SE)

where x-bar is the point estimate (sample mean), t is the critical value from the t-distribution for the desired level of confidence (95% in this case), and SE is the standard error.

However, the necessary data (sample means) for each ethnic group is not provided, so it is not possible to calculate the confidence interval or sketch the graph without additional information.