Location is known to affect the number, of a particular item, sold by an auto parts facility. Two different locations, a and b, are selected on an experimental basis. Location a was observed for 13 days and location b was observed for 18 days. The number of the particular items sold per day was recorded for each location. On average, location a sold 39 of these items with a sample standard deviation of 8 and location b sold 55 of these items with a sample standard deviation of 2. Does the data provide sufficient evidence to conclude that the true mean number of sales at location a is fewer than the true mean number of sales at location b at the 0. 1 level of significance? select the [alternative hypothesis, value of the test statistic].

, μ1 − μ2 ≠ 0 that is true mean number of sales at location a is fewer than the true mean number of sales at location b at the 0. 1 level of significance.

We have given that

For Location A ,

sample size (n₁) = 13

standard deviations (s₁) = 8

sample mean (m₁) = 39

For Location B,

sample size (n₂) = 18

standard deviations (s₂) = 2

sample mean (m₂) = 55

0.1 level of significance implies confidence interval 90% .

90% Confidence interval for μ₁ - μ₂.

A t-test is used when looking at a numeric variable (such as height) and comparing the means of two different populations or groups.

Null Hypothesis

H0: μ₁ -μ₂= 0, where u1 is the first population mean and u2 is her second population mean.

As above, the null hypothesis tends to be no difference between the two population means. Or, more formally, that the difference is zero.

Equation , t =( m₁ - m₂ )/ (√(n₁ -1)s²₁ + (n₂- 1)s²₂)/(n₂ + n₁ - 2)( 1/n₁ + 1/n₂)

=> t = -16 /(√(12×64 + 17×4)/29 )(1/13 - 1/18)

=> t = - 16 /1.9542

=> t = - 8.187

so, basis of t -value the null hypothesis is rejected.

hence , μ₁ − μ₂ ≠ 0 and t = -8.187

To learn more about Null hypothesis on t - statistic, refer:

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Complete question:

Location is known to affect the number, of a particular item, sold by an auto parts facility. Two different locations, A and B, are selected on an experimental basis. Location A was observed for 13 days and location B was observed for 18 days. The number of the particular items sold per day was recorded for each location. On average, location A sold 39 of these items with a sample standard deviation of 8 and location B sold 55 of these items with a sample standard deviation of 2. Does the data provide sufficient evidence to conclude that the true mean number of sales at location A is fewer than the true mean number of sales at location B at the 0.1 level of significance? Select the [Alternative Hypothesis, Value of the Test Statistic].

a) [μ1 − μ2 > 0, t = −7.054]

b) [μ1 − μ2 < 0, t = −7.054]

c) [μ1 − μ2 = 0, -8.186]

d) [μ1 − μ2 ≠ 0, t = −7.054]

e) [μ1 − μ2 ≠ 0, -0.8186]

f) None of the above