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sertanlavr [38]
3 years ago
12

An educational psychologist wishes to know the mean number of words a third grader can read per minute.

Mathematics
1 answer:
Rama09 [41]3 years ago
5 0

Answer: 208.

Step-by-step explanation:

The formula to find the minimum sample size is given by :-

n= (\dfrac{z^*\times \sigma}{E})^2                                    (1)

, where z* = critical z-value (two tailed).                                                                      

\sigma = Standard deviation ( from prior study ) and E = Margin of error.

As per given , we have

Margin of error : E= 0.29

Confidence level = 85%

Significance level =\alpha=1-0.85=0.15

Using z-table , the critical value (two -tailed)=z^*=z_{\alpha/2}=z_{0.15/2}=z_{0.075}=1.439

As per previous study , Variance =\sigma^2=8.41

\sigma=\sqrt{8.41}=2.9

Now, the required minimum sample size = n= (\dfrac{(1.439)\times (2.9)}{0.29})^2   [Substitute the values in formula (1)]

n=(14.39)^2

n=207.0721\approx208  [ Round to the next integer]

Hence, the minimum number of third graders that must be included in a sample = 208.

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