| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2006 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Two-sample z-test large samples |
| Difficulty | Standard +0.3 This is a standard two-sample t-test with large samples (n=70, n=90), requiring routine hypothesis setup, test statistic calculation, and conclusion. The large sample sizes make the normal approximation valid and calculations straightforward. While it requires multiple steps (7 marks), it follows a textbook procedure with no novel insight needed, making it slightly easier than average. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
| Answer | Marks | Guidance |
|---|---|---|
| \(H_0: \mu_A = \mu_B\), \(H_1: \mu_A + \mu_B\) | B1 | \(M_1, \mu_2\) o.k both |
| \(s_c = \sqrt{\frac{u_7^2 + 2s^2}{9}} = \sqrt{27+3412}\) | M1A1 | |
| Test statistic is \(\frac{ | 95-22a | }{s_c} = \) awrt 0.4903 |
| \(cv = \left(\frac{2}{7}\right)1.96\) | B1 | |
| Insufficient evidence to reject \(H_0\), no significant difference between the mean alcohol content of the two samples. | A1N | (Require correct annotation for FF) and/or required |
| Answer | Marks | Guidance |
|---|---|---|
| - require 1 rep from each of 7 to distinctest of diet A to ensure independent, similarly for diet B. | B1, B1 | (2) |
| Answer | Marks |
|---|---|
| B1, B1 | TOTAL 9 |
## Part (a)
$H_0: \mu_A = \mu_B$, $H_1: \mu_A + \mu_B$ | B1 | $M_1, \mu_2$ o.k both
$s_c = \sqrt{\frac{u_7^2 + 2s^2}{9}} = \sqrt{27+3412}$ | M1A1 |
Test statistic is $\frac{|95-22a|}{s_c} = $ awrt 0.4903 | M1A1 | awrt 0.312; 81 point cv 0.025
$cv = \left(\frac{2}{7}\right)1.96$ | B1 |
Insufficient evidence to reject $H_0$, no significant difference between the mean alcohol content of the two samples. | A1N | (Require correct annotation for FF) and/or required
## Part (b)
- require 1 rep from each of 7 to distinctest of diet A to ensure independent, similarly for diet B. | B1, B1 | (2)
- no distincters in manner between the two samples to ensure independent
- not care distincts on diet A and diet B because it it were we need to do a paired analysis.
| B1, B1 | TOTAL 9
---A biologist investigated whether or not the diet of chickens influenced the amount of cholesterol in their eggs. The cholesterol content of 70 eggs selected at random from chickens fed diet A had a mean value of 198 mg and a standard deviation of 47 mg. A random sample of 90 eggs from chickens fed diet B had a mean cholesterol content of 201 mg and a standard deviation of 23 mg.
\begin{enumerate}[label=(\alph*)]
\item Stating your hypotheses clearly and using a 5\% level of significance, test whether or not there is a difference between the mean cholesterol content of eggs laid by chickens fed on these two diets. [7]
\item State, in the context of this question, an assumption you have made in carrying out the test in part (a). [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2006 Q3 [9]}}