Answer:
a. 0.4333
b. 255
Step-by-step explanation:
The maximum Error E is 1.3
approximately normal test scores,
Standard Deviation, SD is 6.5
a).
Level of confidence = 99.7%
critical value of z for a two tailed test and 0.3% level of significance is 3
since the sample mean is within 0.5 of the true population mean
hence, the standard dev of mean is given by
[tex]Z_{\alpha}[\frac{\sigma}{\sqrt{n}} ]=E[/tex]
where E = 1.3
[tex]Z_{\alpha}=[/tex] 1.3
[tex]\frac{\sigma}{\sqrt{n}} =\frac{E}{Z_{\alpha}} \\\\\frac{\sigma}{\sqrt{n}} =\frac{1.3}{3}[/tex]
hence the Std of the mean is 0.4333 (to 4 d.p.)
b).
The sample size is computed as follows
making n the subject of formular of the above equation
[tex]\sqrt{n} =\frac{3\sigma}{1.3}} \\\\\sqrt{n} =\frac{3\times 6.5}{1.3}} \\\\n=(\frac{3\times 6.5}{1.3}})^2[/tex]
hence,
n = 255
