Question

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)

Answer 1

Given,

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

Hypothesized average length: = 26.70

Null hypothesis : H_o : (Claim)

Alternate Hypothesis : H_a : (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.

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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)