# Hypothesis Testing (Z Testing)

A manufacturer believed he can get $1240 for his product. Wanting to prove his belief he collected a random sample of 64 potential buyers of his product and found on average they were willing to pay $1200 with a sample standard deviation of 100. If he tests at the  = .05 level what would he conclude?

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Hypothesis testing (Z testing)

5. A manufacturer believed he can get $1240 for his product. Wanting to prove his belief he collected a random sample of 64 potential buyers of his product and found on average they were willing to pay $1200 with a sample standard deviation of 100. If he tests at the Î± = .05 level what would he conclude?

Solution:

Hull hypothesis:

H0: There is no significant difference in the mean of the product.

H0: Âµ = 1240

Alternative hypothesis:

H1: Âµ â‰ 1240

H1: There is a significant difference in the mean of the product.

Level of significance:

Î± =0.05

Test statistic:

The output is obtained by megastat

Hypothesis Test: Mean vs. Hypothesized Value

1,240.00 hypothesized value

1,200.00 mean product

100.00 std. dev.

12.50 std. error

64 n

-3.20 z

.0014 p-value (two-tailed)

1,175.50 confidence interval 95.% lower

1,224.50 confidence interval 95.% upper

24.50 half-width

Thus the value of the test statistic is -3.20

Conclusion:

Since p-value is less than 0.05 we have no enough evidence to accept the null hypothesis and hence we conclude that there is a significant difference in the mean of the product. i.e., H1: Âµ â‰ 1240

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