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A poll of 1052 Americans showed that 47.4% of the respondents prefer to watch the news rather than read or listen to it. Use those results with a 0.10 significance level to test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it. Use the P-value method. Use the normal distribution as an approximation to the binomial distribution.

Let p denote the population proportion of all Americans who prefer to watch the news rather than read or listen to it. Identify the null and alternative hypotheses.

: p ____   ____

: p ____   ____

(Type integers or decimals. Do not round.)

Identify the test statistic.

z = ____

(Round to two decimal places as needed.)

Identify the P-value.

P-value = ____

(Round to three decimal places as needed.)

State the conclusion about the null hypothesis, as well as State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.

____ the null hypothesis. There ____ sufficient evidence to ____ the claim that fewer than half of Americans prefer to watch the news rather  than read or listen to it.

The minute hand on a watch is 8 mm long and the hour hand is 4 mm long. How fast is the distance between the tips of the hands are changing at one o’clock?