a researcher found that a cigarette smoker smokes on average 31 cigarettes a day. she feels that this average is too high. she s

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8 months ago

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a researcher found that a cigarette smoker smokes on average 31 cigarettes a day. she feels that this average is too high. she s

elected a random sample of 8 smokers and found that the mean number of cigarettes they smoked per day was 28. the sample standard deviation was 2.9. at

Mathematics

1 answer:

Ivenika [448] · Answer 1 · 2024-08-23T00:18:58+03:00

At 0.01 significance level the hypothesis is rejected.

Null Hypothesis (H₀): The sample data occurs purely from chance.

Alternative Hypothesis (H₁): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .01), then we can reject the null hypothesis and conclude that we have sufficient evidence to say that the alternative hypothesis is true.

Given that,

x = 28

s = 2.9

μ = 31

n = 8

α = 0.01

Then, the Null Hypothesis : H₀ = 31

The Alternate Hypothesis : H₁ < 31

The average number of cigeratte smoker per day is less than 31.

Test Statistics:

t = x -μ / s√n

= 28 - 31/ 2.9√8