Question

A national survey indicated that the mean weight of 14-year-old boys was 50 kilograms. In addition, the population was normally distributed. Based on preliminary data, a researcher believes that the average for 14-year-old boys in Maine is different from the national average. To investigate this belief, she randomly samples six 14-year-old boys and records their weights: 44, 47, 45, 48, 49, and 49.

(a) Which statistical test does this scenario call for?

(b) Why that statistical test? Hint: What do we know and what do we not know?

(c) State H0.

(d) State H1.

(e) Please justify your choice of H1.

(f) What are your degrees of freedom (if there are any)?

(g) What is/are the critical value(s) of your test statistic based on $\alpha$ = 0.05

(h) Which of the areas in the figure below (A, B, C, and/or D) reflect the critical region(s)? Select all that apply.

(i) Please calculate the value of each of the following. Hint: Remember, we are now doing inferential statistics.

Sample mean :

Population mean :

Standard deviation :

Standard error :

(i) What is the formula for your test statistic? Hint: It’s probably safer/easier to type it out using parentheses and “ +, -, *, or / ”, but you can write it out in English as well.

(j) What is your obtained value for your test statistic?

(k) What is your p-value?

(l) What is the statistical decision regarding H0?

(m) What is the substantive conclusion? Hint: Be certain that it does not sound like a statistical conclusion.

(n) What is the 95% confidence interval for your estimate of the mean weight of 14-year-old boys in Maine?

(o) In what specific way do the results of (l) and (n) agree?

Answer 1

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