Hypothesis Testing (Z Testing)

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 α = .05 level what would he conclude?
Solution:
Hull hypothesis:
H0: There is no significant difference in the mean of the product.
H0: µ = 1240
Alternative hypothesis:
H1: µ ≠ 1240
H1: There is a significant difference in the mean of the product.
Level of significance:
α =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: µ ≠ 1240

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