Question

The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x = 1.30 A, with a sample standard deviation of s = 0.42 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.)

1. What are we testing in this problem? single mean or single proportion?

(a) What is the level of significance?

2. State the null and alternate hypotheses.

H₀: μ = 0.8; H₁:  μ > 0.8H₀: μ = 0.8; H₁:  μ ≠ 0.8     H₀: μ ≠ 0.8; H₁:  μ = 0.8H₀: p = 0.8; H₁:  p > 0.8H₀: p = 0.8; H₁:  p ≠ 0.8H₀: p ≠ 0.8; H₁:  p = 0.8

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t, since we assume that x has a normal distribution with unknown σ.The standard normal, since we assume that x has a normal distribution with known σ.     The standard normal, since we assume that x has a normal distribution with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Find (or estimate) the P-value.

P-value > 0.2500.125 < P-value < 0.250     0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.     At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the toy company claim of 0.8 A is too low.There is insufficient evidence at the 0.01 level to conclude that the toy company claim of 0.8 A is too low.    

Answer 1

Solution :

Given that

The null and alternative hypothesis is ,

= 0.8

= 1.30

= 0.42

n = 9

( A )

The level ofgnificance

( 0.01 )

This will be left tailed test because the alternative hypothesis is showing a specific direction

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :   = 0.8

Ha : < 0.8

(b) What sampling distribution will you use?

The Student's t, since we assume that x has a normal distribution with unknown σ

Test statistic = z

= ( - ) / / n

= ( 1.30 - 0.8 ) / 0.42 / 9

= 3.57

The test statistic = 3.57

P (Z < 3.57 ) = 0.9998

P-value = 0.9998

= 0.01

0.9998 > 0.01

P-value >

( c )

P-value > 0.2500

( d )

fail to reject the null hypothesis

.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

( e )

There is insufficient evidence at the 0.01 level to conclude that the toy company claim of 0.8 A is too low.