A light bulb manufacturer guarantees that the mean life of a certain type of lig

Question

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 925 hours. A random sample of 35 light bulbs has a mean life of 906 hours with a standard deviation of 75 hours. Do you have enough evidence to reject the manufacturer's claim? Use alpha = 0.09. (a) Identify the null hypothesis and alternative hypothesis. H_0: mu greaterthanorequalto 925 H_a: mu 906 H_0: mu = 906 H_a: mu notequalto 906 H_0: mu > 925 H_a: mu lessthanorequalto 925 H_0: mu notequalto 925 H_a: mu = 925 H_0: mu

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: > 925

Alternative hypothesis: < 925

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.09. The test method is a one-sample z-test.

Analyze sample data. Using sample data, we compute the standard error (SE), and z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 12.68

z = (x - ) / SE

z = - 1.499

z0 = - 1.34

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a z statistic test statistic of - 1.499. We use the z Distribution Calculator to find P(z < - 1.499) = 0.072

Thus the P-value in this analysis is 0.072.

Interpret results. Since the P-value (0.072) is less than the significance level (0.09), we have to reject the null hypothesis.

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