Question

NEEDS TO BE SOLVED WITH A TEMPLATE FOR HYPOTHESIS TESTING IN EXCEL

A company can choose between two brands of light bulbs for an office complex and wants to know if one brand lasts longer than another brand. Test results for the two brands are shown in the table below. Is there persuasive evidence for company officials to conclude at α = 0.05 that there is a difference in the length of life of the lightbulbs?

	n	Life of lightbulbs (hours) (x-bar)	St. Dev. (σ)
Brand A	49	1055	20
Brand B	64	1045	15

a.	Give the null and alternative hypotheses for this test in symbolic form.
		H0:
		H1:
b.	Determine the value of the test statistic.
c.	Determine the appropriate critical value(s).
d	Determine the P-value.
e.	Based upon your work above, should you "Reject the null hypothesis" or "Fail to reject the null hypothesis?" Explain your reasoning.
f.	Is there sufficient statistical evidence to presade the company officilas that there is a difference in the length of the life of the lightbulbs? Explain your reasoning.

Answer 1

Solution-a:

Ho:

Ha:

Ha is claim

Solution-b:

use template

:

https://www.moresteam.com › university › downloads › calculators

In sheet 6:

Two means Z test

Two Means Z-Test							Return To Map
	Instructions:
	1) To obtain the critical values (cut-off values) for your test,							Curve Legend
	enter the desired significance level (a) in the gold cell where noted:								Normal Curve
	2) To obtain the test statistic, p-value, and confidence interval,								2-sided alternative
	enter the requested information in the gold cells where noted:								Less than alternative
	3) Choose the output which corresponds to your alternative hypothesis.								Greater than alternative
	The color of that cell will determine which p-value and confidence								Test statistic
	interval you will use:		2-Sided Alternative (p ≠ p0):		Bitmap Bitmap
			Less-than Alternative (p < p0):
			Greater-than Alternative (p > p0):
Normal Probability Calculator
	(for comparison of means, variances known)
	Enter significance level (a):	0.05
	Cut-off values for:
	2-sided alternative:	-1.960	1.960
	Test Statistic, P-value, and Confidence Interval Calculator						Return To Map
	Enter first sample mean (y-bar1):	1055
	Enter second sample mean (y-bar2):	1045
	Enter difference of interest (D0):	0
	Enter population 1 standard deviation (s1):	20
	Enter population 2 standard deviation (s2):	15
	Enter sample size 1 (n1):	49
	Enter sample size 2 (n2):	64
	Test Statistic (Z0):	2.926
	P-value:
	Two sided alternative:	0.0034

From output

Solution-b:

Z=2.926

Solution-c:

critical values are -1.960 and +1.960

Solution-d:

p=0.0034

Solution-e;

p=0.0034

p<0.05

Reject null hypothesis.

Solutionf:

since p<0.05

Reject null hypothesis.
Accept alternative hypothesis.

at 5% there is sufficient evidence at 5% level of signifcance to support the claim

There is sufficient statistical evidence to presade the company officials that there is a difference in the length of the life of the lightbulbs.