Question

To test Upper H 0​: mu equals 50 versus Upper H 1​: mu less than 50​, a random sample of size n equals 22 is obtained from a population that is known to be normally distributed. Complete parts​ (a) through​ (d) below. LOADING... Click here to view the​ t-Distribution Area in Right Tail. ​(a) If x over bar equals 47.1 and s equals 12.9​, compute the test statistic. t 0 equals nothing ​(Round to three decimal places as​ needed.)

Answer 1

Solution:-

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

Null hypothesis: u = 50
Alternative hypothesis: u < 50

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. 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 = 2.7503
DF = n - 1

D.F = 21
t = (x - u) / SE

t = - 1.054

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 - 1.054.

Thus the P-value in this analysis is 0.153.

Interpret results. Since the P-value (0.153) is greater than the significance level (0.05), we failed to reject the null hypothesis.