The number of people on that program is 6907 ⇒ A
Step-by-step explanation:
The formula of the sample size n is [tex]n=[\frac{p.s}{E}]^{2}[/tex] , where
- P is the critical value of the confidence interval
- s is the population standard deviation
- E is the margin of error
∵ You want to be 95% confident
∵ The critical value of 95% is 1.96
∴ p = 1.96
- We get it by these steps:
- 1 - 95% = 1 - 0.95 = 0.05
- Divide 0.05 by 2 ⇒ 0.05 ÷ 2 = 0.025
- Search for this value in the t table to find p which equivalent to 0.025, you will find it 1.960 (t table is attached)
∵ The sample mean weight loss is within 0.25 lb of the true
population mean
- That means the margin of error is 0.25
∴ E = 0.25
∵ The population standard deviation is 10.6 lb
∴ s = 10.6
- Substitute these values in the formula of n above
∵ [tex]n=[\frac{(1.96).(10.6)}{0.25}]^{2}[/tex]
∴ n = 6906.2748
- Remember we round the number up
∴ n ≅ 6907
The number of people on that program is 6907
Learn more:
You can learn more about the sample size in brainly.com/question/2826639
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