In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8,a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The level of significance is selected to be 0.10. The table "t" value for this problem is _______.
A) 1.318
B) 1.711
C) 2.492
D) 2.797
E) 3.227

Question

Quizplus · Accepted Answer

The test statistic for the two-tailed hypothesis test can be calculated using the formula:

t = (x̄ - μ) / (s / sqrt(n))

where x̄ is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (4.1 - 4.8) / (1.4 / sqrt(25))
t = -2 / 0.28
t = -7.14 (rounded to two decimal places)

The critical values for a two-tailed hypothesis test at level of significance α = 0.10 and degrees of freedom (df) = n-1 = 24 can be found using a t-distribution table. The table "t" value for df = 24 and α/2 = 0.05 is 1.711.

Since the calculated t-value (-7.14) is outside the rejection region defined by the critical values ±1.711, we reject the null hypothesis and conclude that the population mean is not equal to 4.8.

Therefore, the table "t" value for this problem is 1.711 (B).

In Performing a Hypothesis Test Where the Null Hypothesis Is