Question

A phone manufacturer wants to compete in the touch screen phone market. He understands that the lead product has a battery life of just 5 hours. The manufacturer claims that while the new touch screen phone is more expensive, its battery life is more than twice as long as that of the leading product. In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.
Required:
a. Select the relevant null and the alternative hypotheses.
b. Compute the value of the appropriate test statistic.
c. Calculate the critical value to test the phone manufacturer's claim at α = 0.10.
d. What is the conclusion?

Answer 1

Answer:

(a) H₀: μ ≤ 10. vs. Hₐ: μ > 10.

(b) The test statistic value is 1.86.

(c) The critical value to test the phone manufacturer's claim is 1.301.

(d) The battery life of the new touch screen phone is not more than 10 hours.

Step-by-step explanation:

In this case we need to determine the significance of the claim made by the phone manufacturer, that the battery life of the new touch screen phone is more than twice as long as that of the leading product.

The information provided is:

$\bar x=10.5\\s=1.8\\n=45$

(a)

The hypothesis can be defined as follows:

H₀: The battery life of the new touch screen phone is not more than 10 hours, i.e. μ ≤ 10.

Hₐ: The battery life of the new touch screen phone is more than 10 hours, i.e. μ > 10.

(b)

As the population standard deviation is not provided, we will use a t-test for single mean.

Compute the test statistic value as follows:

 $t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{10.5-10}{1.8/\sqrt{45}}=1.86$

The test statistic value is 1.86.

(c)

The significance level of the test is, α = 0.10.

The degrees of freedom will be:

$df=n-1=45-1=44$

Compute the critical value as follows:

$t_{0.10, 44}=1.301$

*Use a t-table for the value.

Thus, the critical value to test the phone manufacturer's claim is 1.301.

(d)

Decision rule:

If the test statistic value is less than the critical value then the null hypothesis will be rejected and vice-versa.

 t = 1.86 > t₀.₁₀, ₄₄ = 1.30

The calculated t-value of the test is more than the critical value.

The null hypothesis will not be rejected.

Thus, it can be concluded that the battery life of the new touch screen phone is not more than 10 hours.