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vladimir1956 [14]
2 years ago
13

Batteries produced by a manufacturing company have had a life expectancy of 135 hours. Because of an improved production process

, the company believes that there has been an increase in the life expectancy of its batteries. A sample of 42 batteries showed an average life of 140 hours. From past information it is known the standard deviation of the population is 24 hours. Test to determine whether there has been an increase in the life expectancy of batteries. What is the test statistic and what conclusion can be made at the.10 level of significance? a. z =.208; Do not reject the null hypothesis b. z =.088; Do not reject the null hypothesis c. z = 1.35; Reject the null hypothesis d. z = 2.33; Reject the null hypothesis
Mathematics
1 answer:
Nikolay [14]2 years ago
5 0

Answer:  c. z = 1.35; Reject the null hypothesis

Step-by-step explanation:

Let \mu be the average life expectancy of its batteries.

As per given , we have

Null hypothesis : H_0 : \mu =135

Alternative hypothesis : H_a : \mu >135

Since H_a is right-tailed and population standard deviation is also known, so we perform right-tailed z-test.

Test statistic : \dfrac{\overlien{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}

where, n= sample size

\overlien{x}= sample mean

\mu= Population mean

\sigma=population standard deviation

For n=42,\ \overline{x}=140\ \&\ \sigma=24, we have

z=\dfrac{140-135}{\dfrac{24}{\sqrt{42}}}=1.35015431217\approx1.35

Critical one-tailed test value for 0.10 significance level :

z_{0.1}=1.28

 Decision : Since critical z value (1.28) < test statistic (1.35), so we reject the null hypothesis .

[When critical value is less than the test statistic value , we reject the null hypothesis .]

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Slope of the line:

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$m=\frac{0-(-4)}{1-0}

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y-intercept of the line is the point where the line crosses at y-axis.

Here, the line crosses at y-axis is (0, -4).

y-intercept, (c) = -4

Equation of a line is

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y = 4x - 4

The equation which matches the graph above is y = 4x - 4.

Option C is the correct answer.

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Subtracting this from the numerator gives a remainder of

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and subtracting this from the previous remainder gives a new remainder of

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This last remainder is exactly the same as the denominator, so x^2+2x+8 divides through it exactly and leaves us with 1.

What we showed here is that

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