Question

In: Statistics and Probability

A business receives supplies of copper tubing where the supplier has said that the average length...

A business receives supplies of copper tubing where the supplier has said that the average length is 26.70 inches so that they will fit into the business’ machines. A random sample of 48 copper tubes finds they have an average length of 26.77 inches. The population standard deviation is assumed to be 0.20 inches. At α=0.05, should the business reject the supplier’s claim?

Yes, since p>α, we fail to reject the null and the null is the claim
No, since p>α, we reject the null and the null is the claim
No, since p>α, we fail to reject the null and the null is the claim
Yes, since p<α, we reject the null and the null is the claim

A consumer analyst reports that the mean life of a certain type of alkaline battery is more than 63 months. Write the null and alternative hypotheses and note which is the claim.

Ho: μ > 63 (claim), Ha: μ ≤ 63
Ho: μ = 63 (claim), Ha: μ ≥ 63
Ho: μ ≤ 63, Ha: μ < 63 (claim)
Ho: μ ≤ 63, Ha: μ > 63 (claim)

Solutions

Expert Solution

Given,

Claim : The supplier has said that the average length is 26.70 inches

Hypothesized average length: = 26.70

Null hypothesis : Ho : (Claim)

Alternate Hypothesis : Ha : (Two tailed)

A random sample of 48 copper tubes finds they have an average length of 26.77 inches. The population standard deviation is assumed to be 0.20 inches.

α=0.05

Sample Size : n= 48

Sample Mean : = 26.77

population standard deviation: = 0.20

As population standard deviation is known,

For Two tailed test :

P(Z<-2.4221)=NORM.S.DIST(-2.4221, TRUE)=0.0077

As P-Value i.e. is less than Level of significance i.e (P-value:0.0154 < 0.05:Level of significance); Reject Null Hypothesis

Ans :

Yes, since p<α, we reject the null and the null is the claim

Using Excel Function to find the P-value : NORM.S.DIST function Returns the standard normal distribution (has a mean of zero and a standard deviation of one).
Use this function in place of a table of standard normal curve areas.Syntax – Standard Normal Distribution

NORM.S.DIST(z,cumulative)
The NORM.S.DIST function syntax has the following arguments:
## Z Required. The value for which you want the distribution.
## Cumulative Required. Cumulative is a logical value that determines the form of the function. If cumulative is TRUE, NORMS.DIST returns the cumulative distribution function; if FALSE, it returns the probability mass function.

---------------------------------------------------------------------------------------------------------------------------------------------------------------

Claim : A consumer analyst reports that the mean life of a certain type of alkaline battery is more than 63 months i.e > 63

The null statement must always contain some form of equality (=, ≤ or ≥)

So therefore ,

Ans :

Ho: μ ≤ 63, Ha: μ > 63 (claim)


Related Solutions

A business receives supplies of copper tubing where the supplier has said that the average length...
A business receives supplies of copper tubing where the supplier has said that the average length is 26.70 inches so that they will fit into the business’ machines. A random sample of 48 copper tubes finds they have an average length of 26.77 inches. The population standard deviation is assumed to be 0.20 inches. At α=0.05, should the business reject the supplier’s claim?
The average length of a maternity stay in a U.S. hospital is said to be 2.2...
The average length of a maternity stay in a U.S. hospital is said to be 2.2 days with a standard deviation of 0.9 days. We randomly survey 80 women who recently bore children in a U.S. hospital. B)Give the distribution of X. (Round your standard deviation to two decimal places.) C)Give the distribution of ΣX. (Round your standard deviation to two decimal places.)
A major coffee supplier has warehouses in Seattle and San Jose. The coffee supplier receives orders...
A major coffee supplier has warehouses in Seattle and San Jose. The coffee supplier receives orders from coffee retailers in Salt Lake City and Reno. The retailer in Salt Lake City needs 550 pounds of coffee, and the retailer in Reno needs 300 pounds of coffee. The Seattle warehouse has 800 pounds available, and the warehouse in San Jose has 650 pounds available. The cost of shipping from Seattle to Salt Lake City is $2.50 per pound, from Seattle to...
Determine the Average Run Length (ARL) of a x-bar chart with limits where the process has...
Determine the Average Run Length (ARL) of a x-bar chart with limits where the process has shifted one standard deviation in one direction
To be considered a wholesaler a business must operate from a fixed location where it receives...
To be considered a wholesaler a business must operate from a fixed location where it receives product from suppliers and ships to its customers. True False The Benning Flower Company operates in the western part of the United States. Its main business is supplying and maintaining floral displays in grocery stores. Every other day a Benning employee visits a store and adds new products while removing older product. Benning is MOST LIKELY a: cash-and-carry wholesaler specialty merchandise wholesaler broker rack...
Copper has 8.5∙1028 free electrons per cubic meter. A 71.0 cm length of 12-gauge copper wire...
Copper has 8.5∙1028 free electrons per cubic meter. A 71.0 cm length of 12-gauge copper wire that is 2.05 mm in diameter carries 4.85 A of current. (a) How much time does it take for an electron to travel the length of the wire? (b) Repeat part (a) for 6-gauge copper wire (diameter 4.12 mm) of the same length that carries the same current. (c) More generally, how does changing the diameter of the wire that carries a given amount...
Sophie has a business where she sells DVDs for $15 each. The average variable cost of...
Sophie has a business where she sells DVDs for $15 each. The average variable cost of production is $10 per unit. The average total cost of production is $16. What should she do in the short run? a. She should continue operating since the business is earning an economic profit. b. She should shut down because the sales are NOT covering the average total cost of production. c. She should shut down since the business is earning zero economic profit....
A thin copper rod has a mass per unit length of 0.1 kg/m. What is the...
A thin copper rod has a mass per unit length of 0.1 kg/m. What is the minimum current in the rod that would allow it to levitate above the ground in a magnetic field of magnitude 0.5 T? (g = 10.0 m/s2) 2.9 A 2.5 A 2.2 A 2.0 A 1.8 A
A rectangular block of copper has sides of length 12 cm, 26 cm, and 37 cm....
A rectangular block of copper has sides of length 12 cm, 26 cm, and 37 cm. If the block is connected to a 5.4 V source across two of its opposite faces, find the following. (a) What is the maximum current the block can carry? (b) What is the minimum current the block can carry?
The Dean of Students at UTC has said that the average grade of UTC students is...
The Dean of Students at UTC has said that the average grade of UTC students is higher than that of the students at GSU. Random samples of grades from the two schools are selected, and the results are shown below. UTC 91) GSU (2) Sample Size 14 12 Sample Mean 2.85 2.61 Sample Standard Deviation 0.40 0.35 Sample Mode 2.5 3.0 At a 0.1 level of significance, conduct a test of hypothesis to assist the Dean evaluate his hypothesis. If...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT