A store that sells televisions buys their televisions from a specific manufactur

Question

A store that sells televisions buys their televisions from a specific manufacturer. The manufacturer claims that only 2% of the televisions they sell have defects, but the manager at the store believes the percentage is actually higher.In the next shipment of 500 televisions, the manager finds that 14 of them are defective. Assume this shipment is a random selection of televisions from the manufacturer. She conducts a hypothesis test where H0: p = 0.02, and HA: p > 0.02 at the alpha = .05 level. She finds the P-value is 0.1007.

Select all that apply.

Select one or more:

a. Since the P-value 0.1007 s higher than 0.05, it is not significant at that level, so we fail to reject the null hypothesis.
b. 0.1007 is the probability that the true proportion of defective televisions is 0.02.
c. Since the P-value 0.1007 is not less than 0.05, it is significant at that level, so we should reject the null hypothesis in favor of the alternative hypothesis.
d. 0.1007 is the probability of having at least 14 defective televisions in a shipment of 500 given that the true proportion of defective televisions is 0.02.
e. 0.1007 is the probability of having at least 14 defective televisions in a shipment of 500 given that the true proportion of defective televisions is greater than 0.02.
f. 0.1007 is the probability of having exactly 14 defective televisions in a shipment of 500 given that the true proportion of defective televisions is 0.02.
g. 0.1007 is the probability of having exactly 14 defective televisions in a shipment of 500 given that the true proportion of defective televisions is greater than 0.02.

Explanation / Answer

Solution:-

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

Null hypothesis: P < 0.02
Alternative hypothesis: P > 0.02

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

The P-value = 0.1007(Given)

Interpret results. Since the P-value (0.1007) is greater than the significance level (0.05), we cannot accept the null hypothesis.

a) Since the P-value 0.1007 s higher than 0.05, it is not significant at that level, so we fail to reject the null hypothesis.

d) 0.1007 is the probability of having at least 14 defective televisions in a shipment of 500 given that the true proportion of defective televisions is 0.02.

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