Question

Use excel

1 A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 52 cables and apply weights to each of them until they break. The 52 cables have a mean breaking weight of 779.1 lb. The standard deviation of the breaking weight for the sample is 15.4 lb. Find the 90% confidence interval to estimate the mean breaking weight for this type cable.

2 According to a Pew Research Center study, in May 2011, 33% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 435 community college students at random and finds that 172 of them have a smart phone. Then in testing the hypotheses:

H0: p = 0.33 versus

Ha: p > 0.33,

what is the test statistic?

Answer 1

Solution:

1)

Using excel,

779.100	mean Sample
15.400	std. dev.
2.136	std. error
52	n
51	df

775.522	confidence interval 90.% lower
782.678	confidence interval 90.% upper
3.578	margin of error

Hence, 90% confidence interval for population mean is 775.5< $\mu$ < 782.7

2)

Using excel,

Observed	Hypothesized
0.4	0.33	p (as decimal)
174/435	144/435	p (as fraction)
174.	143.55	X
435	435	n
	0.0225	std. error
	3.10	z
	.0010	p-value (one-tailed, upper)

Test statistic = z = 3.10

P-value = 0.0010

Here, p-value < 0.05, reject H0.

Conclusion: There is enough evidence to conclude that this percentage is higher among community college students.

Done