The Pew Internet and American Life Project surveyed 351 adults in 2019, asking them about their texting habits. Among men, the mean number of text messages sent per day was 54.2, and among women it was 58.6. Assume that 107 men and 244 women were sampled, and that the standard deviations were 24.3 for men and 20 for women. Can you conclude that the mean number of text messages differs between men and women? Use the a = 0.08 level. a. State the null and alternative hypotheses. Ho: ₁ ✓ H₁: ₁ ✓ 0³ v -3 -2 -1 Critical value(s): = V b. Find the critical value and sketch the rejection region. Sketch of Rejection Region: -1.756, 1.7 x 05 AAA 1 2 3 -3 -2 1 2 3 -3 -2 -1 c. Find the test statistic. -1.773 X H₂ d. Find the p-value. H₂ 0° (If there are two critical values, list both values separated by a comma) 0 1 2 3

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The Pew Internet and American Life Project surveyed 351 adults in 2019, asking them about their texting
habits. Among men, the mean number of text messages sent per day was 54.2, and among women it was
58.6. Assume that 107 men and 244 women were sampled, and that the standard deviations were 24.3 for
men and 20 for women. Can you conclude that the mean number of text messages differs between men
and women? Use the a = 0.08 level.
a. State the null and alternative hypotheses.
Ho: H₁ V
OF H₂
H₁: H₁ ✓
-3 -2 -1 0
b. Find the critical value and sketch the rejection region.
Sketch of Rejection Region:
Critical value(s):
homin
2 3 -3 -2 -1 0
2 3 -3 -2 -1 0
-1.756, 1.7 x
c. Find the test statistic.
= V
-1.773 X
OF
(If there are two critical values, list both values separated by a comma)
d. Find the p-value.
H₂
0.0771 X
2
3
४
Transcribed Image Text:The Pew Internet and American Life Project surveyed 351 adults in 2019, asking them about their texting habits. Among men, the mean number of text messages sent per day was 54.2, and among women it was 58.6. Assume that 107 men and 244 women were sampled, and that the standard deviations were 24.3 for men and 20 for women. Can you conclude that the mean number of text messages differs between men and women? Use the a = 0.08 level. a. State the null and alternative hypotheses. Ho: H₁ V OF H₂ H₁: H₁ ✓ -3 -2 -1 0 b. Find the critical value and sketch the rejection region. Sketch of Rejection Region: Critical value(s): homin 2 3 -3 -2 -1 0 2 3 -3 -2 -1 0 -1.756, 1.7 x c. Find the test statistic. = V -1.773 X OF (If there are two critical values, list both values separated by a comma) d. Find the p-value. H₂ 0.0771 X 2 3 ४
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