Question

assume that a researcher wants to use sample

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u > 5.40
Alternative hypothesis: u < 5.40

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.079901
DF = n - 1

D.F = 43
t = (x - u) / SE

t = -1.75

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of - 1.75.

Thus the P-value in this analysis is 0.044.

Interpret results. Since the P-value (0.044) is greater than the significance level (0.01), we cannot reject the null hypothesis.

(A) Fail to reject H₀, there is not sufficient evidence to support the claim that sample is from the population with a mean less than 5.40.

(A) There is not enough evidence to conclude that the sample is from a population with a mean less than 5.4.