(i) The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below.Age (years) | Percent of Canadian Population | Observed Numberin the Village

Under 5 | 7.2% | 45

5 to 14 | 13.6% | 75

15 to 64 | 67.1% | 286

65 and older | 12.1% | 49

(a) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)

(b) Estimate theP-value of the sample test statistic.

• P-value > 0.100
• 0.050 <P-value < 0.100
• 0.025 <P-value < 0.050
• 0.010 <P-value < 0.025
• 0.005 <P-value < 0.010
• P-value < 0.005

(c) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

• Since theP-value >, we fail to reject the null hypothesis.
• Since theP-value >, we reject the null hypothesis.
• Since theP-value, we reject the null hypothesis.
• Since theP-value, we fail to reject the null hypothesis.

(ii) The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample of 1486 stone tools were obtained from a current excavation site.

Raw Material | Regional Percent of Stone Tools | Observed # of Tools at Current Excavation Site

Basalt | 61.3% | 922

Obsidian | 10.6% | 150

Welded Tuff | 11.4% | 181

Pedernal chert | 13.1% | 184

Other | 3.6% | 49

(a) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

(b) Find or estimate theP-value of the sample test statistic.

• P-value > 0.100
• 0.050 <P-value < 0.100
• 0.025 <P-value < 0.050
• 0.010 <P-value < 0.025
• 0.005 <P-value < 0.010
• P-value < 0.005

(c) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

• Since theP-value >, we fail to reject the null hypothesis.
• Since theP-value >, we reject the null hypothesis.
• Since theP-value, we reject the null hypothesis.
• Since theP-value, we fail to reject the null hypothesis.