Skin care products are big business. A marketing department wants to know whether the age of...

Skin care products are big business. A marketing department wants to know whether the age of a person is related to the importance people place on appearance. They administer an online survey and asked participants How important is “Seeking the utmost attractive appearance” to you using a 7-point scale. Do older people feel as strongly as younger people that personal appearance is important?

	13-19	20-29	30-39	40-49	50-59	60+	Total
7 - Extremely Important	396	337	300	252	142	93	1520
6	325	326	307	254	123	86	1421
5	318	312	317	270	150	106	1473
4- average importance	397	376	403	423	224	210	2033
3	83	83	88	93	54	45	446
2	37	43	53	58	37	45	273
1 - not at all important	40	37	53	56	36	52	274
Total	1596	1514	1521	1406	766	637	7440

If the calculated test statistic is 170.7762, what would the interpretation be using alpha .05?

Expert Solution

Solution:-

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

H₀: The age of a person and importance people place on appearance are independent.
H_a: The age of a person and importance people place on appearance are not independent.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (7 - 1) * (6 - 1)
D.F = 35
E_r,c = (n_r * n_c) / n

Χ² = 170.7762

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than 16.2.

We use the Chi-Square Distribution Calculator to find P(Χ² > 170.76) = less than 0.0001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis. Thus, we conclude that there is a relationship between the age of a person and importance people place on appearance

orchestra answered 2 years ago

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