Question

Tead HW9 MBA EXERCISE HW ASSIGNMENT: HYPOTHESIS TESTING (10 pts.). Name: Suppose a firm producing light bulbs wants to know if it can claim that its light bulbs it produces last 1,000 burning hours (u). To do this, the firm takes a random sample of 100 bulbs and find its average life time (X=980 hrs) and the sample standard deviation s = 80 hrs. If the firm wants to conduct the test at the 5% of significance, what's your final suggestion? (i.e, Should the producer accept the Ho that its light bulbs have a 1,000 burning hrs. at the 1% level of significance?) Ho: = 1,000 hours. Ha: p# 1,000 hours. (3 pts.)

Answer 1

Solution:-

A)

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

Null hypothesis: u = 1000
Alternative hypothesis: u $\neq$ 1000

Note that these hypotheses constitute a two-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 = 8.0

DF = n - 1

D.F = 99
t = (x - u) / SE

t = - 2.50

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.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 99 degrees of freedom is less than -2.50 or greater than 2.50.

Thus, the P-value = 0.014

Interpret results. Since the P-value (0.014) is less than the significance level (0.05), hence we have to reject the null hypothesis.

B)

Thus, the P-value = 0.014

Interpret results. Since the P-value (0.014) is greater than the significance level (0.01), hence we failed to reject the null hypothesis.