7. 6.225-Restaurant Bill by Gender? Use alpha 0.05. Hypothesis statements (use a

Question

7. 6.225-Restaurant Bill by Gender? Use alpha 0.05. Hypothesis statements (use appropriate symbols): a. b. Check the appropriate conditions to conduct the hypothesis test. Note that this was not a random sample. You will need to create histograms using JMP to check some of your conditions. Use the same JMP file as you did with the previous question. h. Compute the degrees of freedom (d). Don't forget to show your calculation. Note if you were to use JMP, which you should not for this question, this df will not match the JMP output as JMP uses a less conservative formula. c. Compute the test statistic by hand using your calculator. d. Find the p-value using Theoretical t distribution from StatKey rounding to 3 decimal places. Include your output from StatKey. p-value Find the p-value using JMP rounding to 4 decimal places. Your answer may differ slightly from 2d) due to rounding error and our conservative estimate of t* however they should be very similar. Include your output from JMP. e. p-value f. Formal decision and why (use the p-value from JMP): Conclusion in the context of this study: g. h. Interpret the p-value (use the p-value from JMP) in the context of this study:

Explanation / Answer

6.225)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: ?1 = ?2
Alternative hypothesis: ?1 ? ?2

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s12/n1) + (s22/n2)]
SE = 4.3731
DF = 46
t = [ (x1 - x2) - d ] / SE

t = 0.16

where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 46 degrees of freedom is more extreme than -0.162; that is, less than -0.162 or greater than 0.162.

Thus, the P-value = 0.87

Interpret results. Since the P-value (0.87) is greater than the significance level (0.05), we have to accept the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that there is difference in mean meal costs of male and females.

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.