Question

The American Pet Products Association (APPA) claims that at least 67% of households own at least one pet. A survey of 102 households show that 63 own at least one pet. At a level of significance of 0.05, does this support the APPA’s claim?

What are the hypotheses for this test?

What tailed test is this hypothesis test?

What is the value of the standardized test statistic associated with these hypotheses? Round your answer to 2 decimal places.

What is the value of the P-value associated with the test statistic? Round your answer to 4 decimal places.

What decision should this P-value result in?

The American Pet Products Association (APPA) claims that at least 67% of households own at least one pet. A survey of 102 households show that 63 own at least one pet. At a level of significance of 0.05, does this support the APPA’s claim?

Consider the following statements relating to the APPA’s claim. Based on your prior results, which of these statements is true?

		The data does not support the APPA’s claim, enough to conclude that the true proportion is at least 67%. The APPA is likely to be incorrect.
		The data does not support the APPA’s claim, but not enough to conclude that the true proportion is less than 67%. We do not know if the APPA is correct.
		The data does not support the APPA’s claim, and we can conclude that the true proportion might be less than 67%. The APPA might be incorrect.

please show work/excel work please

Answer 1

The null hypothesis for this test is

The alternate hypothesis for this test is

This hypothesis is a one-tailed test.

The value of the test statistics is given by

where is the sample proportion of households who own at least one pet.

The value of the standardized test statistics associated with this hypothesis is

The p-value associated with the standardized test statistics is = 0.1314

The significance level is 0.05.

Since the p-value is greater than the significance level, hence this p-value will result in accepting the null hypothesis.

There is not enough evidence to reject APPA's claim even if the data doesn't support APPA's claim. We don't know if APPA is correct. But we can't reject the claim totally because of a lack of evidence. With whatever evidence we have, we can only say that even though the data doesn't support the APPA's claim yet it is not enough to conclude that the true proportion is less than 67%.

The correct option is:

The data doesn't support the APPA's claim, but not enough to conclude that the true proportion is less than 67%. We do not know if the APPA is correct.

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