Question

Asked Nov 11, 2019

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Step 1

Given data

Step 2

**b)**

95% confidence interval is given by

The 100 (1 – *α*) % confidence interval for the population mean, *μ*, for given sample standard deviation, *s* is: (*x̅* – (*tα*/2; *n* – 1) (*s/√n*), *x̅* + (*tα*/2; *n* – 1) (*s/√n*)).

Here, *n* is the sample size, *x̅* is the sample mean, and *tα*/2; *n* – 1 is the critical value of the *t*-distribution with (*n* – 1) degrees of freedom, above which, 100 (*α*/2) % or *α*/2 proportion of the observations lie.

The *t*-distribution is used, because the population standard deviation is unknown and the sample standard deviation is being used as a substitute.

**Calculation:**

Here, *n* = 8; *x̅* = 83.04375; *s* = 11.27021.

Therefore, degrees of freedom = *8* – 1 = 7.

Again, 100 (1 – *α*) % = 95% = 0.95.

Thus, *α* = 0.05.

From the Excel formula: =T.I...

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