Question

To test Upper H0: σ=50 versus Upper H 1 : sigma < 50​, a random sample of size n = 28 is obtained from a population that is known to be normally distributed.

(a) If the sample standard deviation is determined to be s = 35.6​, compute the test statistic. (Round to three decimal places as needed.)

(b) If the researcher decides to test this hypothesis at the α=0.01 level of​ significance, use technology to determine the ​P-value. The P-value is _____. (Round to three decimal places as needed.)

(c) Will the researcher reject the null ​hypothesis? Sine the P value is (less or greater?) than the level of significance, the researcher (will or will not?) reject the null hypothesis.

Answer 1

The null hypothesis and alternative formulated as,

The test is left tailed.

(a): The sample standard deviation (s) is 35.6.

The sample size (n) is 28.

The test statistic is given as,

(b) The significance level is 0.01.

The degrees of freedom (df) = n – 1 = 28 – 1 = 27

The p-value can be obtained by using the Excel function = CHIDIST(x, deg_freedom).

So, p-value = CHIDIST(13.687, 27) = 0.984

Therefore, the obtained p-value is 0.984.

(c): Sine the P value (0.984) is greater than the level of significance 0.01, the researcher will not reject the null hypothesis.