Testing Claims About Proportions. Test the given claim....

Testing Claims About Proportions. Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic,Pvalue or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the Pvaluemethod unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (asdescribed in Part 1 of this section). Smartphone Users A RingCentral survey of 380 smartphone users showed that 152 of them said that their smartphone is the only thing they could not live without. Use a 0.01 significance level to test the claim that fewer than half of smartphone users identify the smartphone as the only thing they could not live without. Do these results apply to the general population?

Testing Claims About Proportions. Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic,Pvalue or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the Pvaluemethod unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (asdescribed in Part 1 of this section).
Smartphone Users A RingCentral survey of 380 smartphone users showed that 152 of them said that their smartphone is the only thing they could
not live without. Use a 0.01 significance level to test the claim that fewer than half of smartphone users identify the smartphone as the only thing they
could not live without. Do these results apply to the general population?

Key Concepts

Null Hypothesis

The null hypothesis is a statement asserting that there is no effect or difference, or that a parameter equals a specific value, and it often represents the status quo. In testing claims about proportions, it typically states that the proportion equals a hypothesized value, forming the basis for the statistical test.

Alternative Hypothesis

The alternative hypothesis is a statement that contradicts the null hypothesis. It specifies the direction of the test (less than, greater than, or not equal to) and represents what the researcher is trying to provide evidence for. In claims about proportions, it suggests that the actual proportion is either lower or higher than the claimed value.

Test Statistic

The test statistic is a numerical value computed from the sample data that summarizes the evidence against the null hypothesis. For proportion tests using the normal approximation, the test statistic is typically calculated as the difference between the observed sample proportion and the hypothesized proportion, normalized by the standard error.

P-value

The P-value is the probability, under the assumption that the null hypothesis is true, of obtaining a test statistic as extreme as or more extreme than the one observed. It is used to decide whether to reject the null hypothesis by comparing it to the significance level.

Significance Level

The significance level, often denoted as alpha (?), is the threshold used to determine whether the test statistic is extreme enough to reject the null hypothesis. It is the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true.

Normal Approximation to the Binomial Distribution

The normal approximation is used when the sample size is large enough that the binomial distribution of the number of successes approximates a normal distribution. This allows for the use of z-tests in proportion testing, based on the Central Limit Theorem.

Generalization to the Population

Generalization refers to the process of applying the results obtained from the sample to the broader population. It involves assessing whether the sample was representative and whether the assumption of randomness and sufficient sample size hold true so that the conclusions can be extended to the entire population.

Transcript

00:01 So in this question of aras, we are asked to use the p -value method to perform an hypothesis test to test the claim that fewer than half of smartphone users identify the smartphone as the only thing they could leave, they could not live without.

00:16 And then we have our sample size.

00:19 So from our data set, we have the sample size to be 380.

00:24 We have a fraction of sample that is the fraction of people that believe that they could not live without your phone to be one.

00:31 Our sample proportion is going to be one one one one hundred one fifty two divided by three eighty and that gives us zero point four which is forty percent and we have our population proportion as zero point five and then we are asked to test to claim that less than 50 percent less than half of the people believe that their phone is something that they could not do without in a day so that means our null hypothesis is that p is actually 0 .5 that is 50 % and the alternative is that p is lesser than 0 .5 so our test statistics is going to be a z test and that is going to be z is equal to the sample proportion minus the population proportion all divided by the square root of p times q divided by n please note that the q is equal to 1 minus p that gives us 1 minus 0 .5 which gives us 0 .5 so it's a it's time to slot in all of those parameters into the formula for the z score so we have that z is going to be 0 .4 minus 0 .5 divided by the square roots of 0 .5 times 0 .5 divided by 380 so 0 .4 minus 0 .5 that gives us minus 0 .1 divided by so i will be using my calculator to calculate to calculate everything here that i have at the denominator that's 0 .5 times 0 .5 divided by 380 and i have this to be 0 .056 approximately to 3 decimal, 4 decimal place rather...

Please give Ace some feedback