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Ivenika [448]
3 years ago
8

Lorraine computed a confidence interval for µ based on a sample of size 41. Since she did not know σ, she used s in her calculat

ions. Lorraine used the normal distribution for the confidence interval instead of a Student's t distribution. Will her interval be longer or shorter than one obtained by using an appropriate Student's t distribution? Explain.
Mathematics
1 answer:
salantis [7]3 years ago
4 0

Answer:

Shorter

Step-by-step explanation:

When given the population standard deviation, σ, the normal distribution should be used. However, if the sample standard deviation is being used, the t distribution should be used. The implication of using a normal distribution in Lorraine's case when using the sample standard deviation which requires the use of the T - distribution is that, the interval beacjbea smaller as the critical value obtained is smaller than the T critical value with degree of freedom, n - 1 ; 41 - 1 = 40

At α = 0.05 ;

Tcritical, df = 40 = 2.02

Zcritical = 1.96

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