A manufacturer of rechargeable laptop batteries markets its...

A manufacturer of rechargeable laptop batteries markets its batteries as having, on average, 500 charges. A consumer group decides to test this claim by assessing the number of times 30 of their laptop batteries can be recharged and finds the average is 497, with a standard deviation of 10. The resulting p-value is 0.1111; thus, the null hypothesis is not rejected. The consumer group concludes that the manufacturer’s claim that its laptop batteries can be recharged, on average, 500 times is accurate. What type of error is possible in this situation? type I type II neither both

Transcript

00:01 In hypothesis testing, you can say two types of testing are there.

00:11 So, here you can say type 1 error occurs when null hypothesis is incorrectly rejected.

00:23 And type 2 error is occurring when the null hypothesis is incorrectly accepted.

00:32 This is rejected, incorrectly rejected and incorrectly accepted.

00:38 So, how you will find it? let us just see in this situation.

00:44 So, the consumer group conducted a hypothesis test to assess the manufacturer's claim that the laptop batteries can be recharged on average 500 times.

00:58 Right.

01:01 So, the resulting p -value is 0 .1111 which is greater than the conventional significance level which is 0 .05.

01:11 Right.

01:12 Assuming a significance number level is 5 percent.

01:16 According to that, 0 .1111 is very large there.

01:19 Right.

01:20 So, since the null hypothesis is not rejected based on the p -value.

01:25 Right.

01:26 So, it is independent of it.

01:28 So, the consumer group concludes that the manufacturer's claim is accurate.

01:37 Right.

01:37 However, it is important to note that the null hypothesis being accurate does not guarantee that the claim is true.

01:46 Right.

01:46 It is simply mean, it simply means that the, that there is not enough evidence to reject the null hypothesis.

01:57 Right.

01:57 So, in case, in this case, the null hypothesis is that the average number of charges is 500.

02:06 Right.

02:07 So, the possible errors could be in two ways.

02:11 First, type 1 error as i already like discussed, type 1 and type 2 error type...

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